cher pas de tout, funny you say it like French will leak out of your ears over time. I know what you mean, but quand même, ça reste dans la tête....

so Luberon, as you may have read on BF already, some of us have been there and its a gorgeous region, I liked it a lot (but was travelling by car with my family and our French friends, we camped there for 2 weeks, not too far from Gordes)
as for the tent. No way you could borrow one? As you know, campgrounds are aplenty, affordable and you could buy a tent with the money you save. As a woman, I sure wouldnt sleep out just on a campmat, heck, I even wouldnt and certainly wouldnt want my daughter to consider it. I guess the camping aspect is really up to you, versus gits or cheap hotels, but if camping does appeal, even camping a few nights could save you the money to be able to buy a small tent. Just saying.

Briwasson's idea of staying in one spot, like Isle-sur-la-Sorgue (very pretty town btw) and doing day trips is a great idea too. Distances arent too much to get to neat sights, so perhaps a cheapish hotel or git could be a base.
Oh, my friends in Normandie tell me that it is already 24c where they are, and Luberon is surely hotter now, so early June will probably already be fairly hot.

good luck with planning.

and good idea to just go do a trip, its good to do things in life if they are manageable and not regret not doing it later.

salut de Montreal