Hi There,
There are all the usual french telecom providers - orange, sfr, numericable, but also successful outside companies such as Digicel.
Often they sell packs including landline, internet, and TV. There are often 40, 60 or 100 destinations included for "free" in these packs - including the US and most European countries.
Most operators cover the majority of the island. 3 G reception can sometimes be difficult due to certain geographic features - they can usually tell you where the trouble spots are. I presume 4 G has been or is currently being installed.
Mobile phone offers often have multi-destination free-call to landlines and sometimes mobile numbers too. Check out a few operators prior to committing to a 12 or 24 month contract. No commitment offers now exist too and can be very interesting. Otherwise you can buy a cheap phone and use rechargeable credit from suppliers like Digicel - Digicel regularly offers a triple-up deal for credit bought over a certain period. Keep listening to the radio !
Hope this helps,
All the best,
Philip