It seems obvious he was asked to leave, not one of them tried to talk him out of it at any stage. As others have said there seemed to be a 'time lapse' between him saying 'fuck off then billy lad' to them all going to bed and him walking out on his own to think in the middle of the night.
I can't imagine those interactions alone would have led to such a 'dark night of the soul'. Something else happened in the interim.
I think he was probably told that he could do it one of two ways- the exit is framed as his decision and he will have the opportunity to leave with dignity or he is removed. The tears I imagine were a combination of feeling ashamed, embarrassed and regret. He seems to lack impulse control - and this pressure cooker environment probably brings out the absolute worst in him.
I am glad he is gone, he and Luca were becoming really quite sinister in their cliquey, controlling ways. Not good for each other at all.
It is more what Gemma doesn't say that what she does say that is enlightening. She didn't once stick up for him, or say 'I know Jacques and he is not being himself'