I think I stayed at Lac D'Orient near Geraudot in the outskirts of Troyes when doing the same trip, I've definitely been there at some point. It's a very popular transit campsite for campervanners and it's not far from the motorway.
I'd definitely recommend taking the lower route through France (Reims, Troyes, Dole) and up into Switzerland neat Bern rather than the upper route (Nancy, Mulhouse) through France and into Switzerland over the hills near Basel. The hills can be a bit of a bottleneck if you get stuck behind a caravan.
If you need to anything about Lauterbrunnen just ask. It's an amazing place.