While Philip Augustus left, I think he left a good number (if not all) of the French Knight he had brought with him under the command of his cousin Hugh III, Duke of Burgundy. So having Philip stay probably doesn't change the situation much in regards to the number of crusaders around.
Of course, Philip wouldn't be in France while Richard is in the Holy Land, so there would be no plot with John Lackland. Without this plot, Richard would probably stay longer in the Holy Land and try his luck.
However, I'm not sure Philip staying is good for the Crusade in terms of leadership. Richard & Philip were originally buddies, but they became ennemies in a short matter of time following Richard's ascension to the throne of England: tensions rose up on the way to the Holy Land (notably because Richard cancelled his engagement to one of Philip's sisters) and, by the time they both took Acre, Philip could no longer stand Richard's attitude (and vice-versa). It's quite likely Philip would argue against some of Richard's decisions.