According to Steve Soares: Monday - Saturday 12:30, 1:40, 2:50 and 5:20.
I would recommend getting a reservation about 40 minutes, but no less than 30 minutes before the start of his rounds. This will allow for extra time if Les Chefs is running behind schedule.
Remy makes a full circuit of the restaurant in about 45 minutes. If you are not at your table when he comes by, he will not come back and you won't be able to walk over to him.
Also he's a highly sophisticated audio-animatronic figure that sometimes has unexpected mechanical problems and won't appear so if you have young children, I would not promise that Remy will be there.