Unfortunately, Amtrak trains do not travel in the Florida panhandle. The closest Amtrak station to Pensacola is in Louisiana, the Slidell Station on the Crescent route. It is about 2.5 hours away via car. You can choose from several rental car companies in Slidell, but you’ll need to call ahead and see if the car rental staff can pick you up from the Amtrak station. There is a nearby Enterprise, and they typically will pick you up if you have a car reservation.
As an alternate, Hattiesburg Amtrak Station in Mississippi is about the same distance from Pensacola (2.5 hours), and has an Enterprise near the station as well. This is the better station because trains arrive before 5 p.m. without delays if you are traveling toward New Orleans.
Otherwise, if you can’t rent a car, Greyhound buses travel between New Orleans and Pensacola. Bus travel time is four to six hours depending on time of day. To reach New Orleans via Amtrak, choose from Crescent trains from New York City/Atlanta, City of New Orleans trains from Chicago/Memphis and Sunset Limited trains from L.A./Texas. You can also rent a car in New Orleans if preferred. Drive time is about three hours. Be sure to check your arrival time in New Orleans as you might need overnight accommodations.