How to travel on budget in France?

I'm a 20 year old girl from Hong Kong. I'm planning to visit France for at least 3 weeks in summer. I plan to visit several different places, with Provence as my focus, but I'll fly to Paris first and visit Giverny. I don't drive, so I'll have to rely on public transport, or my own feet.
I already plan to buy the Rail Europe train pass, and will probably live in 2-star (or below) hotels or youth hostels.
What other ways are there to save money on my trip?
To clarify: the train pass I'm talking about is the France pass.
And yes, I've been to Paris twice before, which is why I'm mainly visiting other places this time.
And Snowman, thanks for the links!

To begin with, unless you plan on spending a lot of time on trains, a Eurail pass is often not much of a bargain. If you intend to travel only in France then a France Rail Pass rather than a Eurail Pass is clearly what you should get.

Next, plan your actual route and take the time to research each destination rather than simply wandering around as the mood strikes you. Budget travel is best accomplished with careful planning.

You will also find that the French hotel star system is a poor indicator of either cost or quality. It is based on the presence or absence of certain physical amenities (elevators, restaurants) and does not evaluate things like cleanliness or staff attitudes.

Might I ask why you are traveling all the way from Hong Kong yet seem to be giving short shift to Paris? Have you been to France before?

EDIT: Okay, that makes it easier to understand your question. It would still be to your advantage to consider where you actually intend to travel within Provencebefore investing in anykind of rail pass.

Provence is, after all, not very large, and therefore distances and train fares are not very big.

There are some good tools to help you budget.

Essentially your main expenses are transport, food and places to stay. You have done you homework with the Eurail train pass - make sure you get the Youth Pass or look into the French and German Rail passes seperately.

http://www.eurail.com/

For accommodation, hostels are charged per bed usually, whereas hotels are per room, which can work out cheaper. Make sure you stay in places that save on transport ie they are centrally located to what you want to do.

Another tip is that you can look for bargains in non touristy areas at the last minute. Be careful, because you always need somewhere to stay, but often business hotels are empty during peak season and offer huge reductions through the last minute offers. Make sure you don't do this in a holiday destination - places book out very early here and you'll pay a lot more for the mistake.

Here's some location directories to save you money on accommodation with sample links:

France Accom :http://www.cheaperthanhotels.co.uk/France/
Paris :http://www.cheaperthanhotels.co.uk/France/Paris/
Giverny :http://www.cheaperthanhotels.co.uk/France/Giverny/
Aix en Provence :http://www.cheaperthanhotels.co.uk/France/Aix-en-Provence/

French Site:
France Accom :http://www.hotelsenfrancais.com/France/
Paris :http://www.hotelsenfrancais.com/France/Paris/

Germany :http://www.cheaperthanhotels.co.uk/Germany

German Site:
http://www.hotelsdeutsche.com/Germany

Other useful tips can be obtained from the official National Tourism websites via these links

France :http://www.tourismrankings.com/France/
Germany: http://www.tourismrankings.com/Germany/

I hope this helps you with your plans.

I'd just stick with youth hostels if you really want to save money. Buy your food at grocery stores and cook in the youth hostel kitchens as much as possible. If you are a student, by all means bring along your student ID so that you can get student discounts. Don't smoke or drink a lot of alcohol. See if some of the attractions you want to visit give reduced rates during the week.

This site lists the best travel bargain sites on the web: http://www.travelstartingpoint.com