World number 204 Vacherot became the lowest-ranked player to reach an ATP Masters 1000 final after he defeated a struggling Djokovic 6-3 6-4.
Hours later, Rinderknech then knocked out former US Open champion Medvedev 4-6, 6-2, 6-4 to complete an extraordinary family double.
"I can't even say it's a dream because I don't think even one person in our family dreamt about it," Rinderknech said about facing his cousin in Sunday's final.
"It was a dream that came out of nowhere."
World number 54 Rinderknech threw caution to the wind after losing the first set to former US Open champion Medvedev, getting an early break and saving five break points in a 12-minute game to go 3-0 up in the second.
Medvedev struggled with the 30-year-old Frenchman's strong returns, finding the net from the baseline multiple times as Rinderknech won the second set 6-2, with Vacherot watching from the stands.
A decisive break secured the third set for Rinderknech, as Medvedev saved the first match point with a 207km serve down the middle, but gave away the second with a double fault.
"I was like, you know what? Maybe I'm going to lose, but I'm going to fight like crazy," Rinderknech said.
"I'm going to make him tired for tomorrow and at least I'm going to help (Valentin) to at least try to start the match a little bit ahead physically.
"Then somehow I got the break and then another one finished the set and then I was like, you know what? I'm just going to try everything and give it my best and somehow it worked out."