I have a gut feeling i know the answer already to this one
if ex wife moves my daughter to France and there is currently a Specific Issue Order and a Prohibited steps order stopping my daughter being called anything other then the name she was registered with when she was born, would the ex be able to set my daughter up in school using a different name as i have been told that the french are quite strict on rules etc...
From what I remember birth certificates are needed to enrol a child for school in France. When there has been a change of name documentation of an agreement between both parents is also required, or a court order granting permission.
Your ex would not be able to enroll your daughter to a French school if you have PR even if there were no orders in place without your written consent or a court order. And no, she cannot change the child''s name without your consent either nomatter where she moves to.
Expect to be soon contacted by your ex asking you written permission to enroll the child to a French school, if she is moving.
Thing is, she is a bit late. As far as I know enrollment is done in May there.