What is the ruling of Islamic law on helping a foreign, atheist entity build a mosque in France, given that Muslims are capable of doing so?

The involvement of non-believers in building a mosque can take three forms:

First: Involvement in responsibility and administration. This is not permissible.

Second: Technical involvement in construction and planning. This should not occur if there are sufficient qualified Muslims, unless there is no alternative. However, if they build a structure and Muslims purchase it, prayer in it is valid if it is clean.

Third: Financial involvement by donating money without any other participation. There is no objection to this, as the Prophet (peace be upon him) accepted gifts from non-believers. It is permissible for a righteous person or a wicked person, a Muslim or a non-believer, to build mosques.