We went to both the Jura and La Bresse this summer, and took the “gentle pootle” options at both.
The Jura does look like the perfect roadie area, lightly trafficed, great views, and some challenging hills. MTB, there are bike parks in the area, mainly in the Eastern part which is hillier, but we didn’t try them. The marked routes are mainly fire-road based with the odd piece of single-track, and fun, but without challenge.
La Bresse in the Vosges is another stunning area, and there’s a bike park just outside the town, which looks great fun, and has a lift. Once again we didn’t ride it, but it wasn’t very busy in the middle of July. As above, the routes on the linked map are mainly fire-roads with some good descents, but nothing too testing. We stuck to blues & reds so the blacks may be different. It does look like the area is a lot more MTB aware, so maybe the locals can help you out? Very busy with roadies, but it’s a lot hillier than the Jura.
Another thread gave details of the 2 different types of marked routes, 1 more biased to fire-roads, the other may have more single-track parts?