Top seed Tsonga seemed to be cruising to his second final of the season but eighth seed Davydenko eventually posed a challenge before Tsonga won 6-0 3-6 6-4.
Davydenko clenched his fist when he finally got on the scoreboard at 1-1 in the second set and he seized on a serving lapse by Tsonga, which included three double faults in the eighth game of the set, to take the match into a decider.
Tsonga, bidding to qualify for the World Tour Finals in London in November for the top eight in the rankings, was made to work hard in the third set.
Davydenko faltered on serve at 4-4 when he made a forehand volley error, allowing Tsonga the chance to wrap up victory.
Earlier, Monfils, who returned to action this week after being sidelined by a knee injury since late May, started strongly against Seppi before losing 3-6 6-1 6-4.
Seppi, the world number 28, completed victory after one hour and 41 minutes on his first match point.
"I am disappointed because the win was within my reach," Monfils told a news conference.
"I lacked freshness, which is normal. But I cannot be satisfied with a semi-final. The hard times have just begun because my body is not used to continued efforts any more."
Former world number seven Monfils, down at 44th in the world rankings because of his injuries, relied on his powerful first serve to grab the first set without giving Seppi a break point.
Seppi fought back to dominate the second set, forcing a visibly tiring Monfils into some extended baseline rallies.
Monfils hung on in the deciding set but the decisive breakthrough came in the fifth game when he stroked a forehand wide to give Seppi the advantage.
Seppi held on to his serve to book his place in Sunday's final, his third of the year.
"It was a tough match, like always," Seppi said. "Especially when you play against Gael in France, it's always tough.
"I did better in the second set and in the end it was more of a fight. We had some very long rallies, especially in the last game. I feel pretty confident and I hope I can recover for the final."