Belgium's Kristof Van Garsse beat Lionel Roux 7-5, 6-4, 1-6, 6-2 in the decisive reverse singles after France had earlier battled back to 2-2 from a 2-0 deficit.
France, who beat Sweden 3-2 to win the Davis Cup in last year's final, had been in the World Group since 1987. They were forced into the qualifying round after they were beaten 4-1 by Australia in the first round of this year's competition in February.
Jonas Bjorkman beat Renzo Furlan and team-mate Thomas Enqvist beat Omar Camporese in yesterday's reverse singles to give Sweden a 4-1 victory over Italy in their Davis Cup semi-final.
"I felt incredibly strong out there," said Bjorkman, who beat Furlan 4-6, 6-4, 6-0, 6-4. "I could have gone on for another hour and a half."
Zimbabwe joined the World Group yesterday by beating a Thomas Muster- led Austria 3-2 in their qualifying round.
The southern African nation can now count itself among the top 16 tennis countries in the World Group, a position they reached for the first time since first competing in the Davis Cup 34 years ago.
Victory was assured in the final reverse singles when Wayne Black came back from losing the first set 5-7 against Gerald Mandl to win 6-3, 6- 3, 6-0. Mandl replaced the Austrian No 2, Gilbert Schaller, who had stomach cramps.
In the other reverse singles, Muster was shocked by Byron Black, finding himself 2-1 down. But his greater power and improving cross-court play brought about the Zimbabwean's downfall with the score at 3-6, 6-3, 2- 6, 6-3, 6-1.
Greg Rusedski has been seeded fourth for the Grand Slam Cup in Munich which starts tomorrow, where he will face Australia's Todd Woodbridge in the first round.
Monica Seles came back from 1-3 in the final set to overpower Arantxa Sanchez Vicario 6-1, 3-6, 7-6 yesterday for her fourth consecutive victory in the Toyota Princess Cup tennis tournament in Tokyo.