for road, due to v few col passes off the Chátel/swiss valleys there arent so many loops you can do.
There’s talk of tarmaccing the road from the col de Bassachaux (end of road SW of Chátel) down to les Lindarets which would open up loads of options for Chátel, and indeed is a plan in order to get the TDF to go to Chátel. (if you’re brave/on a gravel bike, you could descend the gravel track to Lindarets)
There is a loop via Col du Corbier (West of Abondance)
Failing that, you have there-and-backs to places such as Les Crosets, Champoussin, Planachaux etc.