Edmund made his first career final in Marrakech 12 months ago before losing to Pablo Andujar in straight sets.
The Briton returned to Morocco in 2019 hoping to go one better, but Tsonga was too strong as he recorded a 7-6 (8-6) 6-3 victory.
Having edged a tight opening set after a tie-break, Tsonga gained the first break of the match in game five of the second set.
Edmund battled hard to stay in the match but Tsonga's service games were too good and it is the Frenchman who moves onto a quarter-final against qualifier Lorenzo Sonego - the Italian having beaten Robin Haase 7-6 (7-5) 6-3.
Former champion Gilles Simon – who triumphed in 2008 – is also into the last eight thanks to a straight-sets victory over Guido Andreozzi.
Simon's 6-2 6-2 win only took 66 minutes, setting up a meeting with Taro Daniel.