Cost of Living in Lyon, France

I'm not a French expert. But I would guess that prices are going to be highest where incomes are highest. Incomes are generally higher in the North and East.
Incomes are lowest in the Midi or South France (except where there is lot of tourism) and the Massiff Central and probably Normandy. Other not so bad places would likely be southwest France (Bourdeax), along the Loire (Tours, Orleans, Lemans), the Alps (Grenoble), and Burgundy (Dijon).

This summer I was in Tours, Orleans, and Dijon. I kind of looked around at apartment prices and found that nice places (not so large) could be had for under 1000 Euro with some furnished at this price. Minimum stay appeared to be six months. Of those 3 my wife and I preferred Dijon.

When considerng a city I would keep in mind that although the French railway is very extensive it is still very Paris-centric. Non-Paris cities are not so well-connected. That indicates that you might want to locate closer to Paris if you want to travel extensively throughout France. Second, if you are staying the winter remember that as you go East and away from the Meditteranean, it gets colder as you get into more of a continental climate.

Also keep in mind that Paris is really the only world-class city in Paris. The only other cities of more than 1 million I believe are Lyon and Marsielle. Those I mentioned of Tours, Orleans, and Dijon are probably 300-400 thousand. But also keep in mind that French cities and probably European are less sprawling than those of U.S., Canada, and Australia. Orleans has the advantage of being only about 1 hour from Paris. Dijon has the advantage of a connection to Lyon and thus I would guess all of southern france.

If considering the Alps (Grenoble) remember than the Alps have huge long valleys that run East to West I believe. While I don't know what the winter climate is like it's not as rugged as one would believe.

Another option and possibly cheaper is to live in a smaller town closer to one of these regional cities. These small towns can be only 15 minutes by rail to the regional city and many are beautiful and likely even cheaper.