The reason is probably political: to discourage Italian irredentism, the French authorities (in possession of the island since 1768) increasingly reduced the importance of the Italian language, removing it from school education in Corsica in 1860. The course therefore lost the its guiding variant, remaining at the mercy of French centralist policies.
When the issue of course autonomism became topical, it was preferred to give more importance to the local variant rather than to Italian: a choice shared by both the autonomist / independentists and the French central authorities.
In this way, the linguistic question remained an exclusively “internal” fact, and not a matter to be discussed with Italy. Indeed, nowadays, the course is considered one of the regional languages of France: the Corsican linguistic movement has fought for years a very important battle for the dignity of its own speech.
From the linguistic point of view, the current course is very much influenced by French, both in the accent and in the lexicon, which has borrowed many modern words from the official language of the state.