The signed DH route down Semnoz is a little uninspiring (although that was a few years ago and we’d pedalled up so were hoping for a more rewarding trail!). The bus goes from the bus/train station in town, which is the only stop that you were allowed to load a bike on.
There are clearly some decent local trails coming back down Semnoz. Just need to do some exploring.
La Cluzas is 45 mins away and def worth going to for a day if the lifts are open (prob not in May though). Avoid La Grand Bornand as the marked trails there are mostly fireroad.
If the Les Arcs/Bourg St Maurice funicular is running, you could head there for a day (about 90 mins away). The awesome Black 8 runs from top to bottom of the funicular. There are also some other decent ways back down if you follow an OS map.
Check in Annecy tourist info. There are some locally published XC trail routes (sorry i dont have a link to them). The one that hikes up Bluffy, goes across the cliff face and then descends back to the lake by the Angel(?) waterfall is a great natural ride.
Def the best advice is to get an OS map, pedal up a mountain on the road and then pick a downhill footpath. Most are rideable with very little hiking.
Take you own bike. The bikes I rented around there a few years ago were shocking. You do not want underpowered brakes out ther!