Rain delayed play for two hours on Monday, with the big-serving Vukic then missing his moments in two tight sets before Spaniard Pedro Martinez finished in a flurry to win 7-5 6-4 6-0.

Ranked 193 in the world, the Sydneysider had set points in the first and was broken just once in a tight second set before the world No.105 took control.

James Duckworth also lost 6-2 6-3 6-2 on Monday to American Tommy Paul while Millman's match followed a six-hour, five-set marathon and didn't start until after 9pm local time at the traditional day event.

Down two sets and 2-0, Millman showed signs of life to win five straight games against US Open semi-finalist Pablo Carreno Busta.

But the 17th seed returned the favour, the Australian winning just two points in the final three games to fall 6-3 6-2 7-5 and continue his winless record in Paris.

It means no Australian male has won a set in five matches after Alex de Minaur and Jordan Thompson were both comprehensively rolled on day one.

The 24-year-old Vukic's first main draw grand slam appearance was a win in itself though, given it came after saving two match points in the opening round of qualifying.

He is set to rise to a career-high 184 in the world.

"It doesn't matter if you lose in straight or 16-14 in the fifth; it still sucks to lose, but there's positives," he told AAP.

"Best of five sets is a different animal and I'll learn a lot from it.

"This was one of my dreams to play in a slam and I didn't really think I was going to make it this far, especially when down match points in that first qualifying match."

Turning pro two years ago, his run in Paris collected him about $130,000 - a 30 per cent increase in prizemoney on last year for first-round losers and close to half of Vukic's career earnings.

The move was designed to aid the likes of Vukic, who will use the winnings to invest in his game as he eyes the world's top 100.

An aggressive shot-maker, Vukic opted to delay his professional career and attend University of Illinois where he studied finance and dominated the US college tennis circuit.

"I wasn't that good before college, it really helped me because the facilities were incredible and we had great players and coaches," he said.

"It was different again in pros because you're losing every week and it's how you build from that - in the first year I struggled because I didn't lose much in college.

"But you're handling lots of pressure playing in a team ... unless you're actually crushing it, going to college I think is a great pathway."

Vukic will remain in Europe to play more Challenger-level tournaments before returning home for the Australian swing.

Of the 11 Australians in the draw, only Astra Sharma and Daria Gavrilova have so far progressed to the second round.

Former French Open junior champion Alexei Popyrin and Marc Polmans will begin their campaigns on Tuesday.

HOW THE AUSSIES FARED ON DAY TWO OF THE FRENCH OPEN

Aleksandar Vukic lost to Pedro Martinez (ESP) 7-5 6-4 6-0

James Duckworth lost to Tommy Paul (USA) 6-2 6-3 6-2

John Millman lost to Pablo Carreno Busta (ESP) 6-3 6-2 7-5

Australian Associated Press