Leblanc is Mallory's restaurant manager, her right-hand-man who basically acts like her public relations rep and her sidekick, in addition to taking care of her emotional state. It's not exactly an enviable post, particularly earlier in the book, but Leblanc seems fit for the job. For instance, when he comes with Mallory to the Maison Mumbai and she starts crying like a baby, he helps usher her out:
Monsieur Leblanc begged their apologies, paid the bill, pulled the distraught chef up by the elbows, and half dragged the weeping woman back across the street to her restaurant. (7.90)
Phew—thanks, dude. Leblanc's the only one whom Mallory looks at like an equal, as someone she can actually bounce ideas off of and share her vulnerability with. He's usually at her side when she's out and about, but we don't hear a lot about him as an individual.
He's important to the story because he's important to Mallory; she depends upon his even-tempered support and friendship. (There are also suspicions among the other employees about what else their relationship consists of, but there's never any proof.) And he calls her out when no one else does. The most important time this happens is when he literally dumps her out on the side of the road on the way back from visiting Hassan at the hospital, saying:
"You think far to much—about yourself. I am ashamed for you. Now out. I simply can't stand the sight of you right now." (10.31)
It's just what Mallory needs, and when she finally gets home, she is a changed woman, all thanks to Leblanc casting her out to do some good, hard thinking.