Remy begins his circuit of the restaurant at 12:30, 1:40, 2:50 and 5:20 Monday through Saturday. He takes Sunday off.
I would recommend a reservation no later that half an hour before the start of one of his rounds. You must be seated when he comes around - if you are in the process of being seated or you're away from the table (e.g. in the bathroom) you will miss him and he will not come back. You cannot get up and go over to him.
Also, he's a highly sophisticated audio-animatronic figure that sometimes has unexpected problems and does not appear so if you have little ones don't promise that they will see Remy. Let his appearance be a surprise.