France (Paris, Lyon, Arles, Marseille, Annecy, Geneva)

This is possible in 14 days
1. Paris
2 Paris
3.Paris
4.Paris
5. TGV Train Paris to Lyon (takes 2hours 30 minutes)
6.Lyon
7. Lyon
8. TGV Train Lyon to Marseille (takes 2 hours)
9. Marseille
10. Marseille (Day trip to Arles) (takes 30 minutes on train)
11. Train Marseille to Annecy (two trains the connection is at Lyon this takes 5 hours)
12, Annecy
13. Annecy (take a day trip by bus to Chamonix to see Mont Blanc)
14. Train Annecy to Geneva

Cat, if I were planning your trip, the first thing I'd do is go to reiseauskunft.bahn.de/bin/query2.exe/en (not to buy, just to check train duration and connections) to figure out the order of my trip. Just glancing at it, I probably would take the train from Paris to Arles, to Lyon, to Annecy then Geneva. Eventually 3 months or so before the actual train trip, I'd purchase the tickets through the French rail site or trainline.eu/
Actually the other thing I would compare is the flights between the US (or Canada) into Paris, out of Geneva but also into Geneva, out of Paris to figure out the best price and the best connections.

Cat, it's technically possible to visit all these places in 2 weeks, but you are right to suppose that you will have a better time if you pare things back.

What kind of alpine visit do you have in mind? If the idea is to get up close and personal with the mountains then I think you want to go on to Chamonix from Annecy, but if you do that then Provence becomes, in my view, a place too far. One reason for this is you want to spend several full days in Chamonix because the weather is iffy and if you've only allotted one day and it rtrains that day you will have come a long way for nothing.

So you have (in my view) a choice between deep alps and Provence. Here are some possible itineraries:

Deep Alps 1: Paris, Lyon, Annecy, Chamonix, fly home from Geneva.
Deep Alps 2: Paris, Annecy, Chamonix, Lyon, fly home from Lyon or Paris (2 hour train ride to the airport from Lyon).

Provence: Paris, Lyon, Annecy, Arles (or other Rhone Valley town). Fly home from Marseilles or deGaulle (3 hour train ride)

You could also leave Lyon for another trip to allow more time in Provence, but Lyon is a wonderful city.

Provence is a very rich and rewarding region. You could spend a lot of time there and not be bored. If you go for more than a few days I strongly recommend renting a car to explore the region.

Remember the first day on the ground often winds up as a sort of orientation and recovery day that is light on actual sightseeing. Do give yourself enough time to enjoy these wonderful destinations.

Thank you all!!

Just a correction: the trip from Paris to Lyon is about 2 hours (ranges generally from 1h 56m to 2h 6m for the TGV). It's not, as a previous commentator noted, 2h30m (perhaps it's nitpicking, but that's approximately 25 percent longer than reality).
Now, SNCF recommends one be on la voie 2 minutes before departure, so there's that, but still...

As for Chamonix vs. Annecy: I would stay in Chamonix and take a day trip to Annecy rather than the reverse. But then again, I'm a geologist and the alpine glacial landforms visible from the various télépheriques in Chamonix are outstanding.

And for Roman ruins: Lyon has three major Roman ruins and a very good Gallo-Roman museum. Vienne, a little south of Lyon, has a partially-excavated Roman town and a very good museum as well, along with a Roman temple smack in the middle of town. It's worth seeing.