Marné Coetzee represented the Blue Bulls at the Under-19 Grant Khomo Week tournament in 2009, the Under-18 Academy Week tournament in 2010 and the Under-18 Craven Week tournament in 2011. He was part of the South African Schools team. He started for them in their 21–14 victory over France in Port Elizabeth.
After finishing high school, Coetzee moved to Durban to join the Sharks academy. He made eight appearances for the Sharks U19 squad during the 2012 Under-19 Provincial Championship, making eight appearances for this side as they reached the semi-final of the competition before losing 35–46 to the Blue Bulls' U19s.
In 2013, Coetzee played for the South Africa Under-20 team, which attempted to retain the IRB Junior World Championship title they won in 2012. He played off the bench in their opening match as they beat the United States 97–0 and in their next game against England in their 31–24 victory. Coetzee started their final pool match against hosts France.
Coetzee returned to domestic action for the Sharks U21 side in the 2013 Under-21 Provincial Championship, making six appearances off the bench throughout the season. Coetzee's season ended similarly to the Under-19 level the previous year, with his side reaching the semi-finals of the competition before losing to his former side, the Blue Bulls.
Coetzee again represented the Sharks U21 in the 2014 Under-21 Provincial Championship.
In 2015, Coetzee started the season by representing university side UKZN Impi in the 2015 Varsity Shield. He made two appearances for the side that won the competition for the first time. Coetzee missed out on the final stages of that competition as he linked up with the Sharks XV squad for the 2015 Vodacom Cup. He made his first-class debut as a replacement in their 53–0 victory over the Border Bulldogs in their first match in the competition. He started their next game against Western Province. He remained in the starting line-up for the remainder of the competition. Coetzee made seven appearances for the Sharks XV.
Coetzee joined Nelspruit-based side the Pumas on loan for the 2015 Currie Cup Premier Division and made his Currie Cup debut for them by coming on as a replacement in their 20–9 home victory over the Eastern Province Kings. In total, Coetzee played in 62 games for the Pumas.
He also played three games for the SWD Eagles in the 2017 season.
Towards the end of 2021, he joined the Toyota Cheetahs in Bloemfontein. On 26 November 2021, he played in his first match in the Toyota Challenge Series against Romania's Baia Mare at the Toyota Stadium, Bloemfontein. In 2022 Marne was an essential pillar in the Toyota Cheetah machine as he played in eleven of the thirteen Currie Cup matches.