Yes, there are taxis and UBER, but not sure about LIFT. In the smaller villages, I am not certain if you will be able to find an UBER super fast, but there is public transportation. There are also buses. Here are some taxi numbers: https://www.vtc-perpignan.fr https://accueilperpignantaxi.fr/en/contact/ https://www.taxi66.fr/taxi/votre-chauffeur-taxi-pro/accueil-allo-taxi-66 https://www.taxi-stesteve66.fr
Toulouse-Blagnac TLS - 2 hour drive Perpignan PGF - Limited flights here, you can fly from Paris to here or London, for example. Some airlines are Ryan Air for example and can be pretty cheap. Barcelona, Spain BCN - two hour drive If you coordinate with others we can find a way to carpool or shuttle
Civil Ceremony - Reynes, France - nearby towns include Amelie Les Bains, Ceret Main wedding venue - Toulouges, France - nearby to Perpignan
Argeles-sur-mer - Lido beach or Racou Beach Collioure- a port town with a beautiful castle and fort
If you live on the East Coast of US, it may be better to fly out of NYC. So, a flight to NY and then to EU may be way cheaper than a flight directly from your nearest city.
You can take a train that is about 4 hours. You can also fly from Paris to Perpignan. Note that there are maybe limited flights each day from Paris to Perpignan.