OK, now 'indexing' is a perfectly valid term, meaning that something is notched to mark a particular set position

'doigts de passage' --- I am only guessing, but I'm pretty confident that these would be the gear-shifting 'selector forks' --- or more commonly, simply 'selectors'

'axe de sélection de vitesses' gives me more of a problem; does it really mean the 'selector shaft' --- it probably could, though my knowledge of the internal workings of gearboxes is a bit vague. I think I'm right in saying that the intermediate gears slide along lay shafts to engage or disengage the main gears; because the slide, they must presumably be splined onto these shafts, so it seems to me very likely that the problem is that the sliding gear has lost its splines (or they are worn), so sometimes it slips round the shaft instead of being driven by it.

I don't know if I'm wide of the mark, but maybe something there may help a bit! Certainly, worn selectors often do cause gear jumping (don't I know it!)