Abergel obtained his Grandmaster title with the help of the French Chess Federation's structure, which has subsidized training and competition for its best elements for several decades. He is now a trainer himself and has converted to Orthodox Judaism since 1998. His main coach was International Master Jean-Claude Letzelter.
Abergel's significant performances include his participation in the prestigious "B" tournament of the Tata Steel Chess Tournament at Wijk aan Zee, Netherlands, where he achieved 50% of the points. He has also participated in multiple French Championships, notably finishing third in 2011, and the Chess World Cup, but got eliminated in the first round.
In 2015, Abergel took a break from his career and became a coach in Israel for the 'Excellence Chess Center'. The following year, he made a competitive return to the Schachbundesliga championship thanks to the Karlsruhe Ettlingen team.