There are loads of signed trails west of Lyon around Grezieux as Timb34 pointed out.
Polionnay is the focal point of all things Enduro in that immediate area, there are marked open access DH trails in Courzieu.
Southwest of Lyon between the Rhône and St Etienne you’ve got the massif du Pilat which is immense and would need far more research, but would be worth the effort.
Lyon itself has good trail options on the doorstep on Mont d’Or, quite a few dirt spots around the city and an indoor bike park opened up last year in Vaulx en Vélin (Weride)
Check local Facebook groups for group rides as it’s always the best way to learn the trails (chevaliers enduro des monts du lyonnais, Alpina VTT Lyon)