Occitan (Langue d'Oc)and French are not dialects so much as different languages, with some overlap (in my estimation they are further apart than Spanish is from Portuguese). Notwithstanding this, the language at Guerre's trial is specifically mentioned by Zemon-Davis in relation to his re-trial at Toulouse:

[...]and then before the whole Chamber they each had their confrontation with the defendant. There seems to have been no problem with language: the trial was supposed to be conducted "in the vernacular of the area," and all the members of the court were from the region.

The Daguerre family was of Gascon-French Basque background - Martin was born in French Basque lands, but he with his parents moved to Artigat in the Ariège between Toulouse and Foix when he was a child. He would have grown up speaking Occitan there - probably not difficult for his family, as the Gascon dialect of Occitan is pretty close to the Ariègois dialect.

The pretender Martin Guerre's inability to speak Basque however was a subject at trial. Some questioned why he couldn't speak it as his family came from there:

Why had he forgotten so many Basque phrases, some of which must have been bandied about all throughout his childhood?

Others said it was reasonable that he would have forgotten a language that he would only have spoken in the house as a small child:

That the accused knew almost no Basque could mean that he was not Martin Guerre because it was not likely "that a native Basque would not know how to speak his language," or it could simply mean that having left Labourd so young he had never really learned his parents' tongue.

In fact, the questions at trial were less about the pretender Guerre's inability with Basque language than the more provocative lack of remembering certain Basque traditions. The imprint of culture went far deeper for many observers than language:

Then the new Martin started to sell parcels of the propres, a practice not uncommon in the active land market of the Leze valley, as we have seen, but not in accord with Basque custom. When he proposed to put a new lease on some ancestral property in Hendaye, or even to sell it, Pierre Guerre [Martin's uncle] must have been horrified.