I agree - generally the locals tend to eat towards 9:00. In Paris the shops are open to 7:00 and many office workers won't leave work until after 6:00 which means late home with the traffic. So by the time you get out on the town it is after 8:00.
Some very popular restaurants will even have sittings - the first at 7:00, then 9:00 and then at the most popular even 10:30 or 11:00 (Aux Lyonnaise, Chez l'ami Jean for example).
What is the best time? Most difficult to get in between 8:00 and 9:00, easier early or later. I do find the atmosphere different - more tourists early, more locals later. So it depernds on what you want.
Paris restaurants pack in the tables so if you want more space (and less smoke) avoid the peak times. If you want more locals, and thus fewer English voices (and English speakers are often quite loud compared to Parisians) then go for the one in the middle.
When going for dinner, it's earliest 8 PM, but it can also be as late as 9 PM and even later, when going to an event before (like a movie, concert, play, etc.).
Most small bistrots won't even open before 7:30 PM. At brasseries, you won't have that problem though, since lots of them are open nonstop.
If you have small and popular places on your list, it's best to get a reservation as you may get turned away, since everything it booked up as from 8 PM or so.