Hi Moissinac,
I cannot open your website at the moment (here is the error I get “redirected you too many times”).
In order to use WordLift on a multilingual website you will need to run a WordPress instance for each language and two WordLift keys: one for French (the existing one I suppose) and one for English.
We can configure the second key in such a way that if an entity is found by the analysis using the main dataset (French) WordLift will re-create the equivalent entity for English and it will add a sameAs link to the source entity (this way you can keep both graphs connected).
Hope this can help. Write us directly over email if you need further assistance.