Seventh seed Konta is first up on the main showcourt, which tends to be virtually empty for morning matches, against Taiwan's Hsieh Su-wei as she bids to improve on her previous pair of first-round exits in Paris.
Murray, who has been in poor form this season, faces Russian world number 73 Andrey Kuznetsov on the same court but his arrival will be delayed by another rising star, Germany's Alexander Zverev.
The willowy ninth seed, who won the Rome Masters in the build-up to the claycourt grand slam, is locked at one-set all with Spaniard Fernando Verdasco and the pair will play to a finish after their contest was halted on Monday evening.
British number two Kyle Edmund, ranked 49th in the world, is also in first round action, taking on Portugal's Gastao Elias on Court 14.
Meanwhile, 2015 champion Stan Wawrinka opens his campaign against Slovakian Jozef Kovalik on Court Suzanne Lenglen, where the crowd will be awaiting local favourite Gael Monfils.
Monfils, seeded 15th, faces German Dustin Brown in what promises to be an exciting encounter between two of the ATP Tour's more flamboyant players.
(Reporting by Julien Pretot; Editing by John O'Brien)
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