As RayofCommand said, the sentence in question is correct, absolutely and 100 % correct.
(You can also shorten it like this: »Als ich 15 war, lernte ich …« or simply »Mit 15 lernte ich …«.)
However, it would likely be taken to imply that at the age of 15, like some genius or wunderkind, you managed to completely learn French in one straight effort. As we know, learning languages takes time … a lot … you do not completely learn a language in one fell swoop. So what you probably wanted to say is: »Mit 15 fing ich Französisch an.«
On the other hand, take this one: »In der Schule lernte ich Französisch.« This is more realistic, matches our real-world expectations, and doesn't imply any astonishing learning effort.
PS concerning the title of your question, »Expressing processes in the past with “als”«:
There's not the same kind of temporal precision in German tenses as in English or French, where you get things like simple past vs past progressive vs present perferct, or passé composé vs imparfait to express different aspects of past, like momentary or continuous action; however, even though these aspects are not built into tenses in German, they are logically present, of course, just expressed differently, using temporal adverbial expressions, like »neulich« oder »das ganze Jahr« oder »eine Zeit lang« … so what am I trying to get at here? Well, the temporal conjuction »als« implies a momentary action, not a continuous one, with the intent to pinpoint one moment in time, rather than to evoke an ongoing process or lasting state of things.
So, applied to your example, »als ich 15 war«, that's that moment in time right there, and it is unlikely (though not impossible (in the case of a genius)) that you learnt all the French that there is to learn at that age … :)