This is a pretty good price, but generally this is probably a bit early to book so if you waited a few months the price will likely go down.
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This is probably the cheapest flight for layovers under 4 hours. However, if you are willing to do longer stopovers (like 0-48 hours) then I could probably find a cheaper flight.
Do you need 2 checked bags each for a short trip? If you can reduce it to a single checked bag each you can get a direct flight from FLL to CDG for $600 on Norwegian. Departing 3/15 returning 3/19. (Google Flights) This is booking the LowFare+ class for $299 each way including 1 20kg checked bag, a carry on, and a personal item.
Regarding the third party what is the question? In my opinion unless there is a large fare benefit I would always book direct with the carrier. This makes it much easier to deal with any complications should they arise. The exception I have made is with third parties such as Orbitz or Expedia if I'm getting a deal with a bundled price.
If I understand your request you are looking for a one-way back home to Miami AFTER the wedding and don't need airfare to get to LA.
Within the +/- 1 day it looks like you have best fare unless you want to gamble with Spirit (I wouldn't). However, if you are willing to fly on Sunday Jan 5 you can get an early morning direct from LAX to FLL for $201 on Alaska.
If you have tickets already purchased you should first call and see with your original airfare what the cost for moving the departure from Thursday to Tuesday would be with the change fee. (It's not going to be cheap). Unfortunately, if you decide to buy a new ticket you will need to purchase round trip since your return will be voided if it's on the same reservation as the departure.
The fare Snowjunkie21 found is good but with United you'll have to pay a carry-on bag fee. Alternatives are to fly American from either JFK or LGA with a connection for $172 one-way on Nov 26. Fares on Monday are now as low as $102.
Returning on 4/1 will be the most expensive/busiest travel day. If you are flexible to return 3/1 or 5/1 it will be less expensive. The lease expensive option is $2,377 booked with Qatar Airways. (Google Flights) For this booking I have tried to go through to purchase the seat to see the cost of a second checked baggage but don't see that yet.
Spirit and southwest are the only ones that fly nonstop, and you can find the price for southwest on their website
If you are willing to make a couple modifications you can save quite a bit. Returning 8/18-20 is the most expensive. If you could return on 8/21 and also would be willing to fly round trip to EWR you can get a fare as low as $978 per person. The international leg is on United with Air India only covering the domestic portion (1:35). The first checked bags each are included and a second for the 4th bag total would be $100.
You could fly there for 645 roundtrip with a bunch of stops.
This is the first flight and this is the second.
If you want to do this rather than the other option depends just on if how much you value the $150.
Happy to help! I would recommend looking into NOMAD Search on Kiwi.com. Here is an itinerary for your trip on NOMAD totalling $1500
Unfortunately one-way flights are expensive and there is not a great way around it. Hope this helps and have an epic trip!