Can you give me suggestions on where to go on a trip to France?

we stayed in an areas around Cahors..which is kind of central/ southern France. The whole area is really lovely, with lots of medieval villages all around. We hired a car ( as we were staying in the country) and saw lots of little villages....places I highly recommend are: St Cirq lapopie....really lovely and like out a fairytale. On a hill that overlooks the valley below Rocamadour....amazing sight really, a church literlally coming out of a cliff face.....with a little village...you have to take a lift down to it!! Autoire....in the general area of Rocamadour, a lovely little village. There are lots of caves in the area with old rock drawings too and are well worth lookin at. There are other towns and villages scattered all over the place and a French lady said that even for France this area was lovely. Highly Recommended!! You could spend a couple of days in the area sightseeing....we were near the town of Figiac but there are other reasonably sized towns that would be good for accommodation too.

Pars,Versailles,Mont Saint Michel(i'd recomend staying the night and touring it at night), castles(Chambourd), The Alps...just to name a few!

Apart from what you already mentionned like Cote d'Azur try to explore to lovely Provence more once you're there. Don't miss the Loire Valley with all the great castles,beautyful sceneries etc. Will 3 weeks be enough - I doubt it but enjoy the maximum!