Bilinguals have been shown to adapt to syntactic innovations (i.e., structures that deviate from the standard grammar) either by producing such structures more or by processing them faster after repeated exposure. However, research on whether they adapt by increasing their acceptability ratings for innovations is limited. We consider this to be a crucial gap in the literature, since it could provide insights into how speakers adapt their perception for innovations that they might otherwise not adapt to in their production and/or processing. On this basis, the present study investigates overall acceptability and trial-by-trial acceptability (adaptation) for different types of innovations in Canadian French with grammatical structural equivalents in English. Structure type and individual differences in language experience (dominance, proficiency, exposure, etc.) are considered as factors that influence these processes, as previous research has shown that they play a role in the acceptability of innovations in bilinguals. For this purpose, we employed a timed acceptability judgment task (TAJT), where adult bilingual speakers of French and English in Canada were asked to rate innovative sentences in French and their standard (grammatical) counterparts as fast and spontaneously as possible. Both acceptability ratings (offline measure) and response times (RTs) (online measure) across trials were measured to test whether speakers show adaptation on both levels. Results revealed that innovations were rated lower and for most structure types slower than their standard counterparts, with the different types of innovations showing differences. Crucially, adaptation on a group level was reflected only in response times and not in acceptability ratings. On an individual level, though, some participants adapted their ratings, but not consistently across all innovation types. Moreover, ratings and RTs were influenced by individual language experience, with participants with a higher contact with French (higher French Score) being faster and less accepting of innovative sentences compared to participants with a lower contact with French.