[1] Moulai has won three silver medals in his entire sporting career, including one for mixed team relay, and is currently ranked no.

He first competed at both local and national elite championships within a span of ten years in his career, and eventually reached into the international level at his first ITU Triathlon World Cup in Cancun, Mexico in 2004.

During the course of his career, Moulay has further improved on his athletic abilities and physical training after he performed poorly in his first few competitions, and in 2006, he finished astoundingly in twenty-fourth place at the ITU World Championships in Lausanne, Switzerland.

Moulai was selected to the French team for the 2008 Summer Olympics in Beijing; however, he did not finish the entire run in the men's event.

Despite his disappointing finish at the Olympics, Moulai continued to win other triathlon events, by capturing the silver medal at the ITU European Championships in Lisbon, Portugal, and receiving his best result at the ITU World Championships, when he finished eighth overall in Vancouver.