Transition are the Champagne of Bikes 🙂
Reims is a good stop-over, plenty of tours and things to see, tour etc and as you say detour is small. Some of it is a bit touristy but donsome research and maybe ask the Tourist Office for a recommendation of something a bit more special / less formulaic. We use this website for nice B&B’s & Chambre d’Hote (dinner available if pre-booked), worth a search around.
https://www.sawdays.co.uk
We like Burgundy and often stop off there on the way back to buy wine and maybe have a lunch – its about 3 hours from Alps. That’s another option if you want a longer drive the first day. The motorway goes right past Beaune, you could turn off a bit earlier for more village options and to drive past the famous vineyards. Places to stay from above website. Can make sorecific recommendations if you wish. Note if not in a rush and going to Switzerland we take scenic route via small roads in the Jura before getting to Swiss/French border and Lauserne