Is it permissible to submit a personal photo without a head covering to obtain French citizenship? And what is the ruling on acquiring a second nationality alongside one's original nationality?

A Muslim is not permitted to naturalize as a citizen of disbelieving nations, because doing so leads to showing them loyalty. Furthermore, residing in their countries is not permissible except for one who is able to uphold the rituals of his religion and is safe from temptation. The matter becomes even worse for a woman if naturalization requires her photograph while she is uncovering her awrah, such as her hair and neck. This is not permissible except out of necessity.