An independent clause is a set of words that can hold on its own as a sentence. It has a subject, verb and complete thought, as most would say. A dependent clause on the other hand cannot stand on its own.
The answer to this is "She can't study in France.".
Patricia does not know French is not the complete clause, Because Patricia does not know French is an dependent clause easily identified because it starts with BECAUSE and of course BECAUSE is not a clause, it is a subordinating conjunction.
By definition, an independent clause is a sentence that does not need any explaining or any additional sentence structure. The word because does not qualify for that and the same holds for any clause introduced by because; a reason needs to be stated in every such sentence structure. Instead, the clause she cant study in France is self-sufficient and no other syntax is needed; hence this is the independent clause in this case.
