GE will supply five 2.75MW turbines to the Monts du Lomont site near Crosey Le Grande to the north of the region.
The project is being developed by Velocita's French subsidiary in partnership with local developer Opale Energies Naturelles. It will be Velocita's first project to go online in France, which the firm is financing and will build and operate.
According to Velocita, the partnership is developing a portfolio of 23 wind projects with a potential of 750MW. Monts du Lomont is the first phase of a 31MW site. The remaining six turbines will be installed in 2017.
Delivery is expected to take place in the third quarter of 2015, and the project is due online before the end of the year.
It is the first time GE has been contracted to supply the its low-wind 2.75MW turbine with a 120-metre diameter rotor to a project in France.
The Franche-Comte regional government is targeting 600MW of wind capacity by 2020.