While the Italian literary (then national language) and the dialect of the city of Florence and its surroundings went their own way, as they spoke in the rest of Tuscany?
Simple: alongside the official language and that of the capital, the other Tuscan variants continued to flourish and develop, direct local continuators of Latin and closely related to the Florentine. It would be a mistake, in fact, to think that in Tuscany you talk everywhere like in Florence!
Among the different variants, we can remember the Massese, the Lucca, the Pisan, the Sienese, the Livorno, the Arezzo.
Obviously the Tuscan dialects (often called “vernacoli”) all resemble each other, and are all related to the Florentine, but each has its own characteristics, which are often “archaic” to those who are not native to the region.
For example, not all Tuscan dialects have the Florentine gorgia; in other cases, it is so extreme that it almost makes the consonants affected by the phenomenon disappear (this is the case with Livorno).
Depending on the area, the different Tuscan dialects may also be affected by external influences: the Arezzo area has many affinities with Umbrian, while Garfagnino, Versilia and Massese have affinities with the northern dialects.
Also in this case, it is necessary to remember that the influence of the standard language is felt, and that therefore often the more local characteristics have been replaced by other more “Florentine” or “Italian” ones. It is usually easier to find more genuine Tuscan dialects in more rural areas and older people. A common fate, therefore, to that of other “dialects”.
The course, which is spoken in Corsica, in northern Sardinia (Sassari and Gallura) and, in the past, in Caprera, is included in the list of Tuscan dialects. In particular, the variants spoken in Corsica are deeply affected by the ancient contact with Tuscany (especially Pisa).
The relative isolation from the Florentine model has allowed the preservation of some ancient traits, such as the final -u (which in the Tuscan area is present only in some peripheral areas, for example around Mount Amiata, in the Grosseto area), or some grammatical traits that we can find it in the ancient Tuscan and in the dialects of the Centrosud.
However, despite the undoubted kinship of the course with the Tuscan (and therefore Italian), it is considered by many to be a language unto itself.
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.