No one can possibly answer such a broad question. There are more than 40 countries in Europe -- have you narrowed things down at all?

You need to do SOME of the work here.

Sounds doable from my point of view. Do you have any specific questions or doubts regarding the choice of the cities or what to do there?

I'd forget the car - trains are best in Switzerland for areas you are going - for trains to Paris book early for discount fares at www.oui.sncf or www.sbb.ch or www.trainline.com - general info www.seat61.com; BETS-European Rail Experts and www.ricksteves.com. You can take an overnight train between Paris and Venice - www.thello.com.

I also think your trip is doable, and sounds enjoyable. Not too fast but also not lingering too long anywhere. A few more thoughts:
- For order of stops I'd do Paris, Lucerne, Interlaken, Venice and then Rome
- I agree that you don't need a car at all, just use trains.
- Now that you've got the major sites selected, use internet to research top tourist attractions in each location and see what sounds interesting to you
- Watch Rick Steve's Youtube videos on each location as you help narrow down things to do in each location

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Sounds good except for the order. Look on a map. Wouldn't it make more sense to do Paris first. Then Switzerland. Then Italy? The way you have it now has quite a bit of backtracking when Paris is in the middle of the trip (but not the middle of the map -haha).

Yes, I had the same thought about Paris. Starting in Paris would be the best and then Switzerland and Venice.

How old is your child? That would have bearing on hiking in the Alps etc.