The duo defeated Nicolas Mahut (40) and Arthur Rinderknech (27) 6-2 3-6 7-6(1) to secure a 2-1 win in their opening Group C tie. Australia beat Belgium 3-0 in the group's other tie.
Two teams from each of the four groups will advance to the knockout rounds in Malaga from November 22nd-27th.
Germany had lost their previous eight meetings against France and captain Michael Kohlmann was pleased to make "positive history" after their first win over them in 84 years.
"Today was like a roller-coaster, but in the end, it's a big win. It is huge for us," he added.
"I had that question so many times about how many years it is since Germany beat France. I know the numbers and the years were always getting more and more.
"But now we can close this chapter and look forward."
With world number five Alexander Zverev (25) pulling out at the last minute due to injury, Jan-Lennard Struff (32) gave Germany a 1-0 lead in the opening singles by beating Benjamin Bonzi (26) 6-4 2-6 7-5.
But France's Adrian Mannarino (34) levelled the tie with a 6-4 6-3 victory over Oscar Otte (29).
Krawietz and Puetz then held their nerve in the deciding doubles in front of the partisan home crowd.
"Our experience together helps," said Puetz. "We have played quite a few matches together now, including the Olympics, and we are good friends off the court, which always helps.
"On top of that we are two of the best doubles players in the world – we both know that about each other – and that gives us great confidence on top of the wins we have managed together."
