I assume that you have done the research on the feasibility of going to France (visas etc.). Addressing your main question, then, about the expenses and work: I'm not sure how easy it is to get casual work in Paris, I think that if you turn up in person at an establishment you have a chance. However I don't know what visa you are travelling on and whether that allows you to work.
As for expenses, it is possible to live relatively cheaply in Paris if you have a place to cook for yourself. Even eating out can be relatively inexpensive if you choose the right areas. I lived for years in the upper 17th arrondissement (near Metro Brochant) and was spoilt for choice for restaurants: within 10 minutes walk from my apartment I could choose restaurants from 20 or 30 different countries, all affordable (12 to 24 euros for a good meal with wine). Takeaways are considerably cheaper. Public transport is very cheap and very efficient (especially the Metro). Rents are probably comparable to large cities in the US, although you will find that the floor areas are a lot smaller (you get used to that!). If you cooked your own meals and rented a small studio (one-room apartment) in a non-upmarket area (such as the upper 17th or 18th), as a student you could probably manage on 600 to 800 euros/month.
As others have said, it really is not possible for you to move to France as there is no visa that will allow you to live there and pick up unskilled work. You need to know that these visa rules also apply to the other countries you wish to live in.
Non-EU citizens can stay for 90 days out of every 180 days in the Schengen Zone (Google it), and are not allowed to work during that time. It is possible to get a Long-Stay visa, but again you will not be allowed to work and you must prove that you have the money to support yourself. Or, you can apply to study at a university in France, or other European country, and get a Student Visa if accepted, but this quite an expensive prospect.
The only possible way is to study at a European university. There are no work visas for unskilled workers without a university degree
Go study in Germany, university tuition is free no matter what country you are from. However you need to get in and pass a German language fluency exam. Only about 25% of applicants are accepted
Waiter is not a small student job in France, it's a real full salary job and they generally don't hire people who don't have service experience. But even with this experience, it will not help you because unless you have precious skills that can't be found in the rest of the EU, you can't emigrate to France. This will be the same for the other EU countries.
US citizens do not need a visa to visit any of your listed countries as a tourist. However, to stay long term requires a visa. A work visa requires advanced educational and professional qualifications plus the ability to fluently speak/read/write the local language.
The only realistic way for you to stay in Europe long-term as a teenage US citizen is to attend university on a student visa. Really.
Are you planning on specialising in a medical field? Engineering? Or something really rare and hard to find? Because those are the only professions for which employment visas are being granted in EU countries.
If you are not European, you will have to arrange a visa in order to move there legally. European regulations require employers to advertise jobs and demonstrate that there are no viable European candidates for a job before they can offer a position to a non European. In the best of times non-Europeans have to have specialized skills, education and/or experience that cannot be easily duplicated by European job seekers. You're more likely to get a job that takes advantage of your education and skills than an entry level job; however, it's very difficult. Expecting employers to go to the time and expense to get you a work permit when that wouldn't be necessary for European candidates is unrealistic.
Right now, the overall unemployment rate in Italy is around 12% and it's around 37% for young people. In Spain and Greece, the unemployment rate is 27% overall and much higher for young people. In Portugal, the unemployment rate is 18% and France is seeing record high numbers of unemployed people. In the UK, the unemployment rate is 7.8%, but at least the number of jobless fell in June. Sweden is a lkittle higher. The lowest unemployment rates are in Germany, Austria, Denmark and Norway. Right now, the chances are not good, but it might get easier as the economy improves.
My direct experience is with Italy where I lived for the past 13+ years (working for a Swedish company); other countries here in Europe will have similar rules. It's not all that different anywhere else. The site for visas in Italy is: http://www.esteri.it/visti/index_eng.asp . The site has links to the application, the additional information you need to supply in order to get the visa and where to apply. It also includes education visas which are somewhat easier to get than work visas. You can find similar information for other countries on their consulate websites.Visa information on the website of the French Consulate in New York is here: http://www.ambafrance-us.org/spip.php?ru... . You can find other consulate websites with a fairly simple search. Note that you'll need to apply to the consulate that has jurisdiction over the state where you live, but you can find the necessary information on any of the consulate websites.
A work permit is separate - you cannot apply for that yourself in many countries. The company has to apply and they have to be able to demonstrate that there is not a viable EU candidate for the job. As a result, jobs for foreigners including Canadian or US citizens are pretty much restricted to people with special education, knowledge, or experience ... and you would have to be able to speak the local language. However, the level of English is high in Scandinavia and most adults speak it very well. You would be able to manage well while learning the language. Right now, as noted above, the best bet would probably be something in the healthcare field which is a fit for you. When I moved here, it was through a transfer of the job I was already doing in the US to the Italian office. Even so, it took 8 months to put all the paperwork in place to apply for a visa. If you already have a job offer, the company will provide you the information you need for your visa application and take care of things like work permits.
It's useful to check the expat sites for information about living and working in the places you might be interested in. You can find sites by searching for "expat" and the name of your target country. These sites will tell you how to register your address, provide information about healthcare, banks, and so forth to ease you into daily life.
You need to be aware that if you are a US expat, you would need to file tax returns in the US as well as in your host country and that can get to be expensive. You can find cost of living data for Paris and other cities around the world on sites like: http://www.numbeo.com/cost-of-living/cit...
What To Do When Moving To France
More Britons than ever before are taking the bold leap to become expatriates. Moving to a different country can introduce some needed spice and excitement into life, as a new way of life and new cultures are taken in. Large numbers of British expats are relocation to France to start their lives anew; the close proximity to the UK, the vast and beautiful countryside, the relaxing lifestyle and the rich and varied culture are all huge draws. This article will provide advice about what to do when moving to France.
Choose a region
France is a rich and varied country with a number of different towns and region. Each part of the country differs from the others. Some regions contain large cities, while others contain vast amounts of countryside. Some are near to the mountains, while others are close to the sea.
Deciding on which part of France fits your needs is the first step. Examine the job market in the area, the proximity to leisure amenities and, if you are relocating with your family, make sure to research the nearby schools to see if they fit your needs.
Legal issues
Before relocating to France, it's important to make sure your legal standings are in order.
First of all, make sure that your passport is not set to expire within the next 6 months. If it is, contact your local passport office to arrange a renewal.
Secondly, collect any and all legal documents pertaining to your identity. Birth certificates, marriage certificates, employment records, medical records, dental records, academic records and any wills or testaments are essential items that will need to be packed for the move.
Before moving, it's important to contact the tax office and advise them of your relocation, even if you will be maintaining a UK income and a UK bank account. Once in France, a French bank account can be opened, allowing for utilities and other bills to be set up.
Health care
France has a nationalised health service that provides treatment to all its citizens. As an expat, a little work will need to be done to be transferred over to the French NHS.
The first step is to advise your local doctor that you will be relocating abroad. Ask for any and all medical records as they will need to be presented to the doctors in France.
Upon arriving in France, a green health card, or 'carte vitale' as it is known in French, will need to be applied for at the local 'Caisse d'Assurance Maladie'.
In the mean time, while the carte vitale application is being processed, temporary healthcare is available through the European 'E' card system. Your local doctor will be able to provide advice about applying for the 'E' card.
Removals & Storage
After buying a house and arranging any legal requirements, the next step is to organise for any furniture and belongings to be moved to your new home in France.
Specialist removal companies can help to make this process easy. They will visit your home, pack up your belongings and drive them to your new home in France. While this option is relatively pain-free, it can be quite expensive.
The DIY option is a cheaper alternative to hiring professional movers. Simply load up the car and/or rent a van to transport your furniture and belongings and drive them to your new French house yourself.
If you need to leave any belongings behind, storage can be rented to house them. Contact local storage companies to find out how much they cost and then arrange for your belongings to be dropped off there.
Registering with the local mairie
Upon arriving in France, it's important to register your address and your family details with the local mairie. The mairie acts as the bureaucratic hub for a community, and they are able to help with many of the elements of French bureaucracy. Failure to register with the local mairie within 3 months of arriving can carry stiff financial penalties.
Driving in France
Under European law, a British driving license will allow you to drive a car on the roads in France. Many British insurance companies will insure a car to be driven on the French roads but, if you are planning to settle permanently in France, it may be more cost effective in the long run to re-register your car in France. The local mairie will be able to help you complete this task.
Conclusion
Moving to a foreign country can help to spark an exciting new chapter in a one's life. While it may take some work to set up the move initially, with careful planning and preparation, the relocation process will go smoothly without any troubles.
You will have a great experience
No chance