I've figured that Robin and Much served under Henry first, and then were there when Richard became king and showed up. The idea of them being in France opens up some interesting possibilities (I played with a fic idea where Richard did assassinate Henry, and Robin found out), but I haven't been able to reconcile it with show canon. The thing with the assassination is that Richard left Acre on August 22, 1191, and that's the place and year the show sets the attack on him, so it'd have to be before that (unless that date is wrong). It'd be possible that Robin and Much were present for the massacre, but if the assassination was after that, I don't think Robin would've been delirious by the time Richard left. *sighs heavily at the show*

I'm going to make a wildly subjective timeline suggestion here, lol:

August 18, 1191, early morning: Assassination attempt. As marjattak suggested, this prompts Richard to drastic action. This does not happen immediately, as his advisers attempt to talk him out of it.
August 20: Massacre, and Saladin's retaliation. Robin is not doing well, and Much is seeing to him.
August 22: Richard leaves Acre. Robin is fully feverish now.
September-October: Robin recuperates, insists on starting back by late October, before he really should; he may be healed, but is weakened from the extended recovery and illness.
November 1191-April 1192: Trip home is complicated early on by Robin relapsing from pushing himself too hard, and then by winter months. Further delays are met when they stop to stay with friends of Robin's along the way, since they could be expected to visit awhile instead of just staying for a night or two and leaving.

That's just a potential scenario, anyway. ;)