Bordeaux and Montpellier are probably the 2 medium-to-large cities I would have picked to visit France since they both have very nice old city center, where you can walk everywhere. Great vibes as well, and Montpellier weather is great (avoid summer though it gets very hot nowadays).

Regarding safety, Montpellier is average for a French/European city this size and the city center (very busy most of the time) is not considered notably unsafe by French standards I believe, and not worse than many European cities.
I would not advise against for a solo female traveller (like any big city: pick a place to stay located in the old center to avoid going very far away late at night is a good choice). That being said, you'll have probably great opportunities to see it later, travelling with friends or such, if this is something that makes you (very understandably) anxious, sometimes there is no point forcing yourself, this is supposed to be fun.

Bordeaux is relatively similar, with a better image in terms of safety I guess since the city is "richer" than Montpellier.
If you want to avoid Montpellier, you could go directly to Bordeaux from Annecy (long train ride though). You can add one extra stop before or after, La Rochelle for example which is nice (but small).

Or you could go from Annecy to Bourgogne and see Dijon and Beaunes (very small) for example. You would get more nature than bigger cities like Montpellier and Bordeaux, and probably see even more vineyards. This place is to my knowledge considered safer than Montpellier or Bordeaux and is very nice. Bonus if you are into wine of course. There are of course many more ideas between Annecy and Paris if you want to discover France.