Is it permissible to lie to French officials—by claiming to have stayed in France for three months and claiming to not possess identification papers—in order to obtain free treatment for my daughter who suffers from a rare disease?

It is not permissible to lie or scheme to obtain free medical treatment for those who do not meet the conditions, due to the prohibition of lying, deception, fraud, and consuming wealth unjustly. "Whoever cheats is not one of us" (a saying attributed to the Prophet Muhammad).

For someone who enters a non-Muslim country with a grant of security, it is not permissible for him to take anything from their wealth without right. He must either reside there or bear the expenses.

For someone who is well-off, his request for assistance falls under the reprehensible form of begging, unless he requests it from a Muslim state. However, if assistance comes without a request, there is no harm in accepting it, but it is not permissible to lie to obtain it.