I did not comment for a while because I hope that most people get it at the end. Here is the answer.
"Mögen Sie Französisch?" obszön (why? -google it) "Mögen Sie es Französisch?" obszön (why? -google it) More explanation: "Französisch" - in capitals means doing sex the french way. And the word: "mögen" in the sentence underlines that!
"Mögen die französische Sprache?" Do you like French. (or the French language) "Mögen den Klang der französischen Sprache?" Do you like the sound of the French language?
DUO is far from being perfect, and another example to translate an English term to a German one went wrong.
Can I just say that DL's use of "magen" for to like something is just plain weird. I am willing to admit that it is probably a regional variation, but I lived in southern Bavaria, and the word "magen" was only ever used very colloquially to mean to love someone (i mog di'). You would NEVER express liking something, like doing something, or liking someone by using "magen", only expressions such as "gefallen + dative", "etwas gern tun", "etwas gern haben" etc. Even set phrases such as "ich moechte ..." became "ich haette gern". Does any native German speaker agree with me, or is that a purely South German set of expressions?
I see you refer to the verb as magen instead of mögen. Is that Bayerisch? I thought (der) Magen was the stomach (at least in Hoch Deutsch). Not a German speaker but here in Austria people tend to prefer the "ich hätte gerne" over "ich möchte". To give you another example when I was asked the other day if I like driving the person asked "fährst du gerne mit dem Auto?" Instead of using the verb mögen. Still, I wouldn't say that they would not use the verb mögen. Now with your post i'd also like to read the opinion of a native speaker. You have a very good point. I believe Duolingo wants us to learn the verb mögen because as a modal verb is important. Maybe that's why we see it so much here...
UPDATE. I just asked my Austrian husband and he says mögen and gefallen can be used interchangeably, so maybe this is a local thing.