Would an AF Captain know the use of that ACARS printer ?
I can't say if AF captains know how to do this as I don't know any AF captains but as an A330 captain myself, (retired), on our A330's the printout was automatic after setting the park brake and if there were any maintenance messages printed out along with the entire flight summary (times, fuel, etc) we placed them between the thrust levers for either Mtc's awareness, (they would certainly know how to print these messages), and/or the next crew's awareness. Generally the knowledge is not required of flight crews because there are other means to communicate maintenance issues to the next flight crew, (usually the log book, of which an examination is required by the crew before flight).
That said, if the crew wished to know what the ACARS messages were while in flight, that is easy enough to do by navigating to the appropriate ACARS page summarizing these messages and printing that page. I've forgotten the details but it can be done though it isn't an automatic feature in the circumstances AF447 experienced, nor would there be sufficient time to examine the messages. Also, the "Stall" warning from the FWC is not part of the ACARS message system and would not be in any of the ACARS messages.