Historians have hesitated for more than 400 years over the different possible origins of this name. However, they are all based on the traditional claim of the Comtois people to belong to a province having its own character and expressing itself through French language and culture.
A rebel province
According to one tradition, when the Franche-Comté bore the name of Comté de Bourgogne, the Count Rainaud III (1126-1148) demanded independence for the Comté and refused to pay homage to the German Emperor. This earned him the nickname of "Franc Comté" and hence the name of Franche-Comté bestowed on the province.
Franks and free
Another explanation points out the particular situation of the Comté de Bourgogne with relation to the German Empire following its annexation to the latter in 1026. Owing merely military service to the Emperor, the Comté was exempted from taxation and allowed to conserve its language and traditions. This province was thus French and free, earning the name of Franche-Comté.
A French affirmation
In 1861, Auguste Castan the historian affirms that the written name of "Franche-Comté" first appeared in a charter dating from the year 1366, and then written "France Comté". According to him, it was the Countess Marguerite, who, on coming into possession of the Comté de Bourgogne, introduced this expression into official documents. Marguerite was a French princess, daughter of the King of France, Philippe Le Long. Influenced by the French councillors advising her, she seems to have wished to make it clear in this way that the region was for her, in fact rather than by right, a French province. In the 15th century, the term "France Comté" became "France-Comté", for, during this period, official acts were drawn up in Flanders, where the "c" is pronounced "ch" (2).
Bibliography :
(1) Edmond Péclin - Histoire de la Franche-Comté - "Que sais-je ?"
(2) Mémoires de la Société d'Emulation du Doubs - Year 1861 - Page 493