I should point out that when I had dinner on the Bateaux-Mouches, food was served inside; it wasn't the open-air experience portrayed in Charade. We took the Bateaux-Mouches in May, and there were a multitude of flying insects who would have made dining al fresco impossible - and I gather the situation is the same no matter what month you're in Paris.
But dinner was served in a glass enclosed area, so the views were still wonderful.