From Jerome, Anne and Stefan
I have some experience with traveling to France for Vacations and racing once.
Bringing your bike is great because you can use it whenever you want. However, you need to carry it with you. A compact soft case, like the orucase IMO is better as it fits in almost any car or train but it require to remove the fork and the derailleur but not the chain. You also need to remove all batteries except if there are embedded and CO2 cartridge. It is convenient to travel with a small pump.
If you plan to bike for a single set of continuous days, I recommend renting too. If so, take your bike fit measure and possibly your shoes, pedals, and saddle.
As I usually visit families and friends to find rides, I visit the local store and look at existing rides on Garmin Connect or Strava (using the heatmap). I usually do some loop coming back to the starting point. You will possibly need to upload a new map in your Garmin as they are often loaded with only the map of the continent where you bought it. If so, go to https://extract.bbbike.org/
Several sites to look at
I have no experience in Swiss or Croatia, but I spent a few days in the Alps close to Embrun (known for the Embrunman) at a resort called Vacances Bleues, which is simple, with healthy breakfast and dinner. I didn't eat there for lunch as I was on my bike looking for bakeries. I liked that my bike was stored in a room with many other bikes. Many cyclists stayed for a night or multiple days during my stay.
Another well-known resort is called Belambra. I saw the sign in the ski resort Les Saisies. There is a new one in Tignes (both are famous ski resorts). I never tried, but you can compare prices and check if they also handle bikes.
Biking in the French Alps is excellent and easy, with a very respectful and supportive community.