Iberia Travel Listing Lake Fausse Pointe State Park Lake Fausse Pointe State Park About: Daily. Beautiful park located adjacent to America’s largest river swamp, the Atchafalaya Basin. Primitive, glamping and RV campsites, cabins, picnic tables and pavilions, splash pad, fishing, nature trails, boat and canoe rentals. Where: 5400 Levee Rd. St. Martinville, LA 70582 (337) 229-4764 Visit Website Location Details