LaFleur attended Westlake High School, where he played tight end and defensive end. He also practiced basketball and track. As a junior, he had 31 receptions for 657 yards and 8 touchdowns. In his last year, he posted 31 receptions for 652 yards and 5 touchdowns, while being named the Louisiana High Schoolplayer of the year, All-American, and being part of the USA Today All-USA high school football team. He finished his high school career with 81 receptions for 1,758 yards and 18 touchdowns.
College career
LaFleur accepted a football scholarship from Louisiana State University. As a redshirt freshman he played in every game with his first start coming against the University of Florida, while making 8 receptions for 59 yards. His blocking was so impressive, that as a sophomore after having only 21 receptions for 263 yards and 2 touchdowns, he was still voted All-SEC. He also was the first Tiger tight end since 1984 to score twice in a game, as he recorded 3 receptions for 59 yards with touchdown receptions of 35 and 12 yards against the University of Southern Mississippi. As a junior, he registered 12 receptions for 120 yards, after missing 3 games with a knee injury. As a senior, he had 30 catches for 439 yards and 3 touchdowns, becoming the first school tight end to lead the team in receiving since 1980. At the end of the season, he was named All-American, All-SEC, LSU offensive MVP and played in the Senior Bowl. He finished his career with 71 receptions for 881 yards and 5 touchdowns, while starting 28 out of his final 30 games and being active in a total of 41 contests.
Professional career
After the team's offense suffered because of the health of Jay Novacek and the lack of production at tight end, the Dallas Cowboys were determined to solve the situation in the 1997 NFL Draft, even going as far as soliciting quarterback's Troy Aikman input in private workouts of the two top ranked players at the position: Tony Gonzalez and LaFleur, that were reported by the Sports Illustrated magazine. It was eventually published in the media that both the Cowboys and Aikman, had him rated ahead of Gonzalez, because they considered him to possess a rare combination of skills. The Cowboys traded up with the Philadelphia Eagles moving from the 25th to the 22nd position, in exchange for third and fifth round draft choices, to select LaFleur in the first round. In his rookie year he mostly blocked for the team, but his receiving production was disappointing. In 1998, he was named the starter, posting 20 receptions for 176 yards and 2 touchdowns. Against the New Orleans Saints, he suffered a sprained PCL in his right knee, which forced him to miss the last 3 games. He returned in the playoffs against the Arizona Cardinals, but did not record a reception in the 7-20 loss. In 1999, during the offseason he suffered a broken right fibula in mini camp and underwent a microscopic lumbar discectomy to repair a herniated disc. He still was able to have the best season of his short career, registering 35 receptions for 322 yards, while leading the NFCtight ends and his team with 7 touchdowns, becoming just the second tight end in franchise history to reach this number. Besides a groin injury that affected him during the season, LaFleur had back problems that dated back to his college years and it started to affect his play in 2000, when he registered 12 receptions for 109 yards and one touchdown. LaFleur was waived injured on August 22, 2001, when he couldn't pass a physical exam. He finished his career with 85 receptions for 729 yards and 12 touchdowns.