The collapse is happening just as the Marne is kicking off on the 5th. Sarrail, thinking he can salvage the situation, doesn't inform Joffre immediately of his predicamate. As a result, the offensive kicks off on time, but the 6th army is short 2 corps. A couple of reserve divisions are on the way to the 3rd army, so they can help shore up the line. Once committed, Joffre can't call it off, namely for moral, as once his soldiers think the retreat is over, telling them otherwise is not a good idea.
Also, I imagine he is hoping that an offensive success elsewhere in the line can offset the disaster near the Argonne. Joffre seems like an "offensive is the best defense" kind of guy, so even if he knew of Sarrail's problem, me thinks he would still order the fight anyway.
De Castelnau really doesn't have a choice about his defensive stance, when threatened on both sides and with limited forces, he doesn't really have the chance for the Napoleonic "defeat in detail". It looks like the 1st army is going to have to give up some more troops.