Can Fransican priests be allowed to perform an exorcism with a bishops approval and do Fransican priests perform exorcisms?
It doesn’t matter if the priest is a diocese priest or if he belongs to a religious order. All priests and deacons do a minor exorcism when they are baptising a person. It is part of the Baptism rite.
When it comes to “major” exorcisms, what matters if he has the bishops permission, follows the proper preparations and the exorcism rite. The bishop has appointed a priest, or several depending upon the diocese, to do the exorcisms. Contacts are first with your parish priest.