Finally, I found a method to diagnose my constantly crashing firefox, and actually, the solution has been there all the time. Thanks to Mozilla crash reporter.
Input about : crashes in the location bar, I got a list of reported crashes, picked some of them, and Mozilla gave me this nice report. The “related bugs” item shows that the problem may come from two plugins. After turning them off, and re-openning the firefox, it has been smooth ever after !