Fenninger was fastest at downhill practice on Friday, stopping the clock at one minute and 45.93 seconds, while Slovenia's Maze finished 10th with 1:46.85.
After nine races for the ladies in the 2015 FIS Alpine Skiing World Cup, Maze leads Fenninger by 257 points in the overall standings, while the Slovenian is also on top in the downhill with Fenninger in third behind second-placed Lindsey Vonn.
But after Friday's strong performance, Fenninger is confident she can make a move in France.
"The training went well for me," Fenninger told fis-ski.com.
"I thought the course would be faster, I was a bit surprised coming down. We had to stay focused while waiting at the start, which I managed to do.
"Hopefully I can perform well tomorrow as well."
Despite having finished second overall in the downhill last season, Fenninger has never won a race in the discipline, with giant slalom her specialty.
But the 25-year-old Austrian also finished second overall in super-G last year and, with Sunday's race at Val d'Isere in that discipline, Fenninger could be set for a top weekend.
Fenninger's compatriot Regina Sterz was just 0.42secs slower in training on Friday, while Vonn finished third after going wide on one turn.
"I think I was a little bit nervous after Stephanie Moser's crash," Vonn said.
"Everyone was having troubles with the jump. I didn't ski my best. I went pretty wide in one of the turns.
"But for that mistake it was a pretty fast run and that gives me confidence for tomorrow."
Vonn is second overall in the downhill and super-G standings after impressive performances at Lake Louise in Canada in December, while Maze claimed a win and a second-place finish in Sweden last week.