If a toy can help you learn French, does it have a French-teaching function, a French-learning function, a French-teaching facility, or a French-learning facility?
I'd appreciate your help.
A toy that helps you learn French has
a French-learning use
a French-learning application
a French-teaching function
a French-teaching facility
a French-teaching capability
Function, facility, and capability are intrinsic to the thing. use and application are extrinsic.
Use and application refer to what others can do with it. Function, facility, and capability refer to what it does.
The professor teaches (or tries to do so); the student learns (if he hopes to pass the final examination). Those two words have very distinct meanings. In your example, "teaching" is correct, and "learning" is not.
"Facility" has several meanings: "easy skill" is probably the one intended. But it is a poor choice because a toy does not distinguish between easy and hard, and any skill employed was that of the human designer and artificer rather than of the mechanical result.
"Function" also has several meanings, but one is "purpose," which is apt in this case. So of the four, "French-teaching function" is the only correct choice. It is grammatical and idiomatic. It will be understood and even welcomed among designers and product marketing managers, who speak that kind of jargon. If you want to talk to normal people, say "an entertaining toy that teaches French."