If [I see a] job I could do, even though I don't meet the stated requirements, should I apply anyway?Short answer: yes.
Longer answer: companies are all over the map here, although in general the less layers of bureaucracy there are between the team that the candidate will work with and the hiring process, the more likely the list of requirements is to be actual requirements.
How can you tell?
HR paper pushers like to think in terms of checklists because that lets them go through hundreds of resumes without any real understanding of the position, so they write ads like this one -- lots of really specific "5+ years of X," not much about what the position actually involves.
But if it's the team lead himself writing the description, which you will see at smaller companies, then you get much more about what the position involves and less checklist items, because the lead is comfortable determining competence based on skill instead of pattern matching. For a software development position, I don't care if you have a degree in CS if you can code. (Open-source contributions are a better signal for ability and passion than a degree, anyway.) My team has people with no degree, to people with PhDs.
Even when dealing with large companies, you have to factor in that people are terrible at distinguishing "want" from "need." A lot of "requirements" are really "nice-to-haves." It can be tough to tell the difference, but the better idea you have of what the job actually involves, the better you can tell which are hard requirements.
For instance: without knowing anything else about a position, my guess is that "native French speaker" really would be a hard requirement. That's not the sort of thing people tend to put down on a whim. But even then, there are shades of grey. For instance, if I were looking for a job and found a "distributed databases developer position, must know Java, be familiar with open source and be a native French speaker" then I might see if they'd give me a pass on the last part because I'm a really good fit for the rest -- and I know they're unlikely to find a lot of candidates with an exact match.
In short, you have little to lose by trying, but don't just shotgun out resumes; include a cover letter that highlights the best matches from your experience to what they are looking for. Follow up with the hiring manager if possible to ask (a) "I sent in my resume a few days ago, and I wanted to see where you are in the hiring process for this position," and if they reply that they got it but you're not a good fit, ask (b) what specifically they were looking for, so you can flesh out your intuition that much more for next time.