Serbian tennis star Novak Djokovic at US Open (AP)
World number one Djokovic split from Marian Vajda after last year's ATP Finals having worked with the Slovakian coach since he was a teenager in 2006. They took a break from each in other in 2017 but reunited the next year.
Molcan and Vajda started working together earlier this month.
Djokovic eased to victory in round one in his first Grand Slam match since losing last year's US Open final, but standing in the way of a record-equalling 21st major are both potentially Nadal and Alcaraz in the second week.
"The draw is the draw. You can't really affect it. It's a matter of luck or some other force interfering with who is going to come to which side and quarter and semi and whatever," said Djokovic.
"I did look at the draw. I think we all do. But at the end of the day, you always have to turn your attention to only the next challenge."
Chasing a 14th French Open title, Nadal goes up against French wildcard Corentin Moutet in the evening session. Moutet knocked out 2015 champion Stan Wawrinka in round one.
Nadal began the year with a 20-match winning run, capturing a second Australian Open title to claim a record 21st Grand Slam and move ahead of Djokovic and Roger Federer.
The 35-year-old's record at the French Open stands at a staggering 106 wins and just three losses since his 2005 title-winning debut, but he is without a title on clay this season after dealing with rib and foot injuries.
"Of course the confidence is higher when you win Monte Carlo, Barcelona, Madrid, or Rome," said Nadal.
"When you are winning more matches and more tournaments you have better confidence. The opponents feels that too, and at the end, you are more used to the level that you need to play to win matches.
"When this is not the case, things are different."
Alcaraz, 19, is attempting to become just the eighth teenager to capture a major men's title, and widely tipped to break the stranglehold of Djokovic and Nadal.
He is the tour's dominant player in 2022, posting a 29-3 record and winning a season-leading four titles.
Three of his triumphs have come on clay in Rio, Barcelona and Madrid where he defeated Nadal, Djokovic and world number three Alexander Zverev to hoist the trophy.
He faces fellow Spaniard Albert Ramos-Vinolas for a place in the last 32.
Zverev, a Roland Garros semi-finalist in 2021, takes on Sebastian Baez of Argentina. The 21-year-old Baez won his maiden title at Estoril at the start of the month.
Greek fourth seed Maria Sakkari, who was a point away from reaching the final here 12 months ago, takes on Karolina Muchova of the Czech Republic.
Reigning US Open champion Emma Raducanu plays Aliaksandra Sasnovich in round two, while Bianca Andreescu, the 2019 winner at Flushing Meadows, faces Olympic champion Belinda Bencic.
Two-time former Australian Open winner Victoria Azarenka meets Germany's Andrea Petkovic, who made the last four in Paris eight years ago.
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