The Danish player had a six-shot lead overnight, but he slipped from 15-under to 12-under.
Coetzee -- a five-time European tour winner -- was third overnight and the South African's 3-under 68 put him in contention at 11-under after Hojgaard's early blunders.
Hojgaard made a quintuple-bogey on the par-three second hole and a bogey on the next. It was far removed from Thursday's first round, when his 9-under 62 tied the course record at Le Golf National outside Paris.
He steadied himself, however, with two birdies on the front nine. Although he made three more birdies on the back nine, he also bogied twice, including a demoralising one on the 18th.
Belgian Thomas Pieters carded a 5-under 66 to join Barjon (70) on 10-under and go into Sunday's final round tied for third place.
The tournament was not played over the past two years due to the coronavirus pandemic.