Probably not.
Dr Jonathan Landis, Director of the Center of Middle East Studies at the University of Oklahoma, searched for the source of the story and provides a well-reasoned analysis of the evidence in a 2016 blog article:
A reporter, Maria Rosette Shapira, who was attached to the French force, covered both events for the French weekly, L’Illustration. Shapira, who wrote under the pseudonym Myriam Harry, described the battle of Maysaloun and, briefly, Goybet’s arrival in Damascus in an article published on 21 August. It is her follow-up piece, which was printed on 11 September, that is of interest, because it hints that Goybet may have said something that caused offence.
[...]
Unless a definitive eye-witness emerges, Harry’s reportage suggests that it was Goybet, rather than Gouraud, who is more likely to have made the notorious remark.