Awang, Malaysia's flag-bearer at the Beijing Olympics, claimed a deserved silver medal with another Frenchman, Kevin Sireau, beating Australian Shane Perkins to the bronze.
The men's sprint tournament is traditionally the most coveted of all track cycling events, and it lived up to that billing thanks to the unexpected rise of Awang to the final.
After Bauge had been given the decision from a photo finish in the first leg of their final, the tactically astute Awang forced the match into a decider after outwitting Bauge in the second leg.
In the decider, however, Bauge took no chances, forcing an early lead on his smaller rival and using all his power to charge towards a convincing win.
Bauge, based in Creteil near Paris and trained by French track legend Florian Rousseua, thus succeeded absent Sir Chris Hoy, the British Olympic champion who is currently injured, to take his first world gold in the sprint.
After being given a scare by Awang, Bauge's cries of joy and relief echoed around the velodrome as he handed France - who for years dominated the event - their first world crown since Laurent Gane in 2003.
Bauge admitted he had to dig deep to overcome his sprint rival, whom he said was as "cunning as a monkey".
"I let myself be sucked in by his tactics in the second leg, but the first one was very close as well," said Bauge.
"He's wily, and I knew it, but when you're on the bike it goes so fast that you have very little time to react.
"In the decider I had no option but to take the match to him and sprint like I know how to."
Asked what this title signifies, Bauge added: "After I crossed the finish the first thing I thought was, 'God is great'.
"I'm succeeding a long list of big champions. Now, I have no option but to look forward to the Olympics."
Given that he came to Poland hoping to perform well in the keirin, Awang could be happy with sprint silver, Malaysia's second medal of the championships following Mohd Rizal Tisin's historic bronze in the kilometre.
But the 21-year-old, who was adopted out to a more financially comfortable family by his poor parents when he was a baby, felt that without a crucial error in the decider he could have caused a major upset.
"I'm still happy with my silver medal. It's not too bad, but I'm a little bit sad because I knew I could do it," Awang told AFP.
"After I drew the second match I felt I had the legs to do it, but sometimes we make mistakes, right?
"I made a mistake during my last ride and I couldn't get the speed up that I needed."
Asked how his achievement will be met in his home country, Awang added: "I think everyone's happy. Especially as we came here not really thinking about medals, we just wanted to perform well and break a few national records.
"For me to get the silver and Mohd to get the bronze in the kilometre is a big bonus for Malaysia, and for Asia."
Source: AFP Global Edition