But there was disappointment for Alexei Popyrin who followed his fellow Sydneysider onto Court 1 at La Defence Arena but lost to No.13 seed Alexander Bublik 6-4 6-3.
The Kazakh, who served 13 aces to Popyrin's three, crucially broke at 5-4 in the first set. Popyrin answered an early break in the second stanza, but could not respond again when Bublik broke for 4-2
That ended the prospect of the two Australians meeting in the third round, though that was already long odds as Vukic, ranked 103 in the world, now meets fourth seed Taylor Fritz.
The American, who received a first round bye, is fourth in the world and has won all three matches with Vukic.
Nevertheless, Vukic has reason for confidence after dismissing locally supported Atmane, who is 69th in the world having climbed more than 100 places in the last six months - and beat Fritz in Cincinnati in August.
Both players achieved three breaks, but whereas Vukic broke once each set Atmane could only break in the second.
Whoever wins between Vukic and Fritz, should they also progress through the third round, is then lined up to meet the other Australian in Paris, Alex de Minaur, in the quarter-finals.
The national No.1 is seeded sixth and, after a first round bye, will play 25th-seeded Dutchman Tallon Griekspoor or Canada's Gabriel Diallo.
He should then face 10th-seeded Karen Khachanov, tricky Canadian Denis Shapovalov, or rising star Joao Fonseca, the 19-year-old with the pulverising forehand who won the ATP 500 in Basle on Sunday.
The one player de Minaur will be relieved to know he cannot face until the final is Jannik Sinner, who extended his dominance over Demon to 12 wins out of 12 in the Vienna Open semi-final on Saturday.
Mind you, he will probably have to beat world No.1 Carlos Alcaraz, who is in de MInaur's half of the draw, to reach the Paris final.
The Spaniard will play Cameron Norrie in the second round after the Briton beat Sebastian Baez 6-3 6-4.
Among other matches Andrey Rublev beat Jacob Fearnley 6-1 6-4, Flavio Cobolli beat Tomas Machac 6-1 6-4 and wildcard Arthur Rinderknech beat Fabian Marozsan 7-5 (7-5) 7-6 (7-4).
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