You cannot drive from Louisiana to Cancún. The Gulf of Mexico separates them—no roads, bridges, or ferries connect the US mainland to the Yucatán Peninsula.
Drive to Houston (IAH/HOU) (~3.5 hrs, 220 mi) or New Orleans (MSY) (~2 hrs, 130 mi) for more flight options/lower fares.
Check travel.state.gov for Mexico advisories. Quintana Roo (Cancún) often Level 2: Exercise Increased Caution (crime). Resort zones generally safer. Enroll in STEP.
Cancún is a flight away—not a road trip.