The drive from Paris to Chamonix is lovely, rolling hills, small villages with church steeples peeking up. Not exciting terrain but, having driven both, it is much more interesting than Colorado to Iowa. The French highways are in excellent shape and the restareas (aires) generally have fresh espresso or capachino and good pastries and some have full restaurants.
It is easy to drive away from Paris and Wil gave great driving instructions.
The exit signs in Europe generally show a city far far away rather than the next town, confusing at first but think "direction Lille" vs. "Lille is at this exit". Not unlike seeing a sign for Omaha or Chicago when leaving Denver, it is a good leason in geography, a paper map can help with understanding these signs. GPS is also good but via.michellin is better, look up the route before you go and you can put in closer towns to fine tune the gps suggestions.
Also stay in the right lane except when passing and have euro coins and bils for the tolls.
Eveyone is different with thier response to jet lag, you may be fine - especially if you sleep on the plane. It may not hit you until the next day and by then you will be in Chamonix! If you are exhausted just stop at a lovely aire or walk in a small village, or if you are really spacy give up, get a hotel and continue the next day. Driving in Europe is great fun and much more flexible than the train.
Enjoy the trip!