This is do-able. However, you must have a plan to do it "right."
Yes, you can watch the fireworks from New Orleans Square (where Fantasmic! takes place); however, you will NOT get to experience it to its fullest.
The Remember, Dreams Come True fireworks show has LOTS of very cool effects that are seen on Main Street, but not at the Rivers of America (NOS). Particularly, there are effects on / with the Castle that can only be seen from Main Street.
IF you want to see the fireworks from Main Street and Fantasmic!, the easy way is to do them on different nights. The way to see them both on the same night is as follows...
Note: You stated in your post that Fantasmic! is at 9p and 10p. It is not. It is at 9p and 10:30p.
1. Get to Main Street early to get a spot for the fireworks show. You want to get a spot on the left side of Main Street (facing the castle) near the Hub. This is important.
2. Watch the fireworks show.
3. The SECOND the show ends (9:45p), you need to walk quickly towards the entrance of Frontierland. There will be 1,000s of people doing the same thing. There will also be 1,000s of people coming out of that area from the 9:00p Fantasmic! show. Keep your group together and just keep walking. (We do a single file, all hold hands line. LOL) Stay to the right as you walk towards the River. It will be VERY crowded.
4. Once you get to the riverfront, other guests will already be there. Kindness to others goes a LONG way. find spot near the center of the island (it'll make sense when you see it). It will probably be about 10:10 - 10:15. Get settled and wait for the 10:30pm Fantasmic!
It's not easy, you have to deal with MAJOR crowd movement, but it's do-able and gives you a great view of both shows.
- Dreams