Vacherot, who defeated Frenchman Rinderknech in Shanghai to become the first player from Monaco to win an ATP title, cruised past 14th seed Jiri Lehecka 6-1, 6-3 in the first round in Paris on Tuesday.
"I'm living a fairytale... that's why I'm playing so well, I'm enjoying every second," said Vacherot, who was 204th in the world when he became the lowest-ranked player to win an ATP Masters 1000 tournament.
Rinderknech, a wildcard in the tournament like his cousin, beat Fabian Marozsan 7-6(5), 7-6(4) on Monday to reach the second round.
"This time I am the first one to play and (Vacherot) has to follow suit. I prefer it this way, because it was tiring in Shanghai," Rinderknech said.
Vacherot said he was proud of how Rinderknech had played against Marozsan.
"It was such a tough match against Fabian... I'm just so excited for the crowd, for the family. We're just going to enjoy this match so much, once again," he added.