I would do LD Lines from Portsmouth to Le Havre and as you've got kids, just hack across France on the autoroutes (As there is only a certain amount of Are we there yets?" that anyone can listen to)
Although my kids have both been very good, it is a bit of a journey and plan your journey so that you do have somewhere for them to play, run around etc etc etc.
It is fairly easy to navigate your way around Paris, but if you live in fear of the stories about Paris, then cut down to Orleans, then across to Troyes, and then beyond.
I presume it is Divonne near Geneva - Otherwise you might be going the wrong way
The French are arrogant on the road (I speak as a half Frenchman) but they are just very confident on the roads and as long as you let them in when they are car hopping then all is okay. They mean no harm at all. It's just there way.
As for parking. The French tend to leave their handbrakes off (ON flat roads) so you can bump in and out of a spare space. I leave my brake on though as I have a Merc. Van from Motability and I don't think my insurance policy would be valid!!!
Please, please, please try and speak some French - The French will love you for it, but if you make no effort they will just ignore you. They are proud people.