The answer is would be the first one
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.
The correct answer is The alligator slipped quietly into the water.
The first sentence does not agree since alligators should be a singular form, while the second and third are nonsensical because of lack of information.
Option 1 is the correct answer