The defeat at Docklands stadium came with a sting in the tail for France, however, with Selma Bacha falling awkwardly in stoppage time and carried off on a stretcher with an apparent lower leg injury.
Fowler's composed 66th-minute strike in front of 50,629 fans at Docklands stadium settled the Matildas' nerves after captain Sam Kerr and strike partner Caitlin Foord were subbed off near the hour-mark after a fruitless hour in front of goal.
The crowd was an Australian record for a women's soccer match, smashing the previous best of 36,109 in 2021, when the Matildas hosted the United States in Sydney.
The mark will only last six days as more than 80,000 are expected at Sydney's Stadium Australia for the co-hosts' World Cup opener against Ireland next Thursday.
Apart from Bacha's injury worry, France, who first play Jamaica, may leave Melbourne feeling a touch aggrieved after striker Eugenie Le Sommer was pounded in the back by Steph Catley in the area but denied a penalty near the hour-mark.
Tony Gustavsson's Australia played an energetic game, harrying the French all over the field but could conjure few shots on goal until Hayley Raso found space on the right wing and found Fowler with a cut-back pass.
Fowler slid home a low shot to trigger huge cheers around the roofed stadium.
Gustavsson sprung a couple of selection surprises, with Cortnee Vine starting on the wing and fit-again Alanna Kennedy at centre back alongside Clare Hunt.
France boss Herve Renard kept faith with the starting 11 that beat Ireland 3-0 in their recent friendly in Dublin but had Elisa De Almeida at centre back in place of Estelle Cascarino.
In a scrappy opening, neither team could convert chances, with Kenza Dali firing wide from the edge of the box and a heavy touch by Kerr failing to honour a sublime through-ball from Foord on the break.
With France making inroads down the Matildas' left flank, Grace Geyoro pounced on a meek headed clearance and thumped a volley goalwards but it cannoned into the outstretched leg of Hunt.
