Hi Albert,
Both solo and towing, I've used the start of the route you describe - but split off just after Langres to drive along the D67 through Champlitte and Gray to Besancon (more like an N road), and then take the E23 to Pontarlier and Lausanne.
Good hotel in Champlittle (solo) or river side camping at Gray.
The start of the E23 out of Besancon is the issue with this route - a single track road that climbs out of the river valley. Our Mercedes C270 CDI towing an Eriba Triton was fine, but that's no surprise with 180 bhp / 410 NM torque towing a 1000 kg 3-berth Eriba (about a 50% match).
I'm guessing you'll be much closer to the 85% guideline, but HGV have no problem.
However, you may want to evaluate the route with www.viamichelin.co.uk and when you do, click "options" or "customise your route" and set your car type, fuel and typical costs, that you have a caravan and whether you prefer motorways or not. This also recommends the route you mentioned.
If you prefer the motorway route, then my wife has driven that route on the way to meeting in Chalon sur Soane from Geneva airport - and says the road is OK - but can't remember if caravans are restricted from the tunnel. But there is an N road that parallels that tunnel - just looks like it would take an hour to drive around.
Robert