Alcaraz is targeting his first French Open title, having already won the US Open and Wimbledon.
But his preparations were hampered by a forearm injury which he carried into the clay-court major.
He arrived in Paris with only a run to the Madrid Open quarter-finals under his belt on clay and he admitted earlier in the tournament that he was still feeling pain.
After powering past Sebastian Korda in the third round he said he felt more like himself – and he looked it as he beat 23-year-old Auger-Aliassime on Court Philippe Chatrier.
“I didn’t come here with a lot of rhythm but I believe in myself. After every practice and every match I’m getting better,” Alcaraz, who reached the semi-finals last year, added.
Auger-Aliassime needed treatment for what appeared to be a muscular issue early in the second set and struggled with his serve for the remainder of the match.
With Auger-Aliassime vulnerable, Alcaraz broke twice on his way to a 5-0 third-set lead and served out victory shortly after Tsitsipas had done the same on Court Suzanne Lenglen.
Arnaldi had stunned Russian sixth seed Andrey Rublev in the previous round and led by a set and a break as he looked to take another notable scalp.
Tsitsipas, who lost to Novak Djokovic in the 2021 final at Roland Garros, was made to pay for not taking any of five break points in the first set and another three in the second.
However, he showed courage to save four set points at 5-3 and 5-4 and was rewarded by eventually breaking Arnaldi’s serve in the 10th game.
After winning the tie-break and breaking in the first game of the third set, Tsitsipas retained utter control and broke three more times to race away with victory.