Thank you both for your interesting comments. As with Howards End, I think Eric is going for a sedate, comfortable life with Henry. I kind of wish Lopez had just made Henry a garden-variety rich-ish guy rather than stack the deck and make him a billionaire with a $250 million annual income who is as attractive as Hickey. But I guess it's easier this way for Eric to take the compromise of the safe refuge of Henry without realizing he's making that compromise. (Although I don't seem to remember Eric ever mulling over that compromise after he accepts the proposal.)
I am having trouble remembering: when Henry brings up the idea of Eric going to Paris with him, is it clear that Henry means that Eric should be going as his romantic partner, rather than a continuation of their current, close-but-platonic relationship? I didn't have the impression Eric thought of Henry as a romantic partner prior to Henry's out-of-the-blue marriage proposal, but I could be mis-remembering.