Is it permissible to accept gifts from a sister who is married to a non-Muslim and resides in France, knowing that our mother is aware of this and is displeased with her daughter?

The marriage of a Muslim woman to a non-Muslim is unanimously forbidden, based on Allah's saying: "And do not marry [your daughters] to idolaters until they believe." If a woman does this, knowing it is forbidden and deeming it permissible, she has apostatized. She must separate from her husband immediately, because it is considered adultery. She must also repent. If her husband embraces Islam during her 'iddah (waiting period), then he has more right to her. As for dealing with her, it depends on what serves the best interest, and maintaining or breaking ties with her depends on what achieves righteousness.