If you have space in your suitcase, take small quantities of basics eg washing up liquid, tin foil, cling film, kitchen towel, (take out the cardboard centre and flatten, ditto toilet rolls -just a few) salt, pepper, tea, coffee, soap, spices, etc, so that you don't have to buy large amounts from the local supermarkets. Chemists such as Boots etc have small plastic containers for sale, or decant into sealable plastic bags. Take a couple of bin bags, rather than having to buy a whole roll.
Check with the tourist office, online before you go, and when you get there to see if there are any special price tickets you can get for local buses or trains.
If it applies, check out any under 25 or over 60 deals.
Look up the museums or art galleries you may be planning on visiting - they often have a free afternoon. Take ID such as driving licence on such visits, (leave passport in apartment), as there is usually a discount for EU member countries.
Eat and drink at the bar - the price increases greatly if you sit in the nice seats outside watching the world go by.
There will be a local market daily for fruit, veg, meat and fish - much cheaper than supermarkets. There will almost certainly be a stall selling wine. See what other people are bringing to get filled up and copy.
The water in France is perfectly good to drink, but if you're not happy with it, boil up a kettle or saucepan, allow to cool and then keep in the fridge, (and to top up your carrying bottle).
Lunch in restaurants is almost always cheaper than dinner - have sandwiches or an omelette in the evening.
Take a small medical pack, aspirin Rennies, band aids, etc.
When you see what you have been able to save, you can go a bit mad once or twice. And, finally, check out what other people say on sites such as TripAdvisor - they don't just talk about hotels, they often mention useful places to Save a bit.
Hope this helps.