Your profile suggests Bristol based (as I am too), you can easily get to Grenoble or AdH in a day (i’ve done it twice) with a chunnel about 11am and arriving sometime around 11pm.
So there’s a decent hostel in grenoble:
https://www.hihostels.com/hostels/grenoble-echirolles
Where it’s ok to arrive fairly late, or if you want to stop 2 nights and get some riding in, try les bergers (you can call them and arrange to get keys left in a safe if late) in Alp D’huez – search my previous posts on AdH threads for route suggestions. If you’re racing 24hrs you can presumably handle some climbs, I can recommend some good big loops.
Alternatively I’ve stopped over in Freiburg (near Baden Baden as suggested above) and in nearby villages when going to Italy via ferries to Bruges.