Sometimes the most natural and compelling director-star tandems come completely by surprise.

Take Olivier Assayas, the highly regarded French filmmaker best known for making contemporary dramas with elliptical overtones, and Kristen Stewart, Hollywood A-lister and a one-time franchise icon, who has gone in a completely different direction since her “Twilight” days ended.

It’s not an intuitive connection, but over the course of two films — 2014’s “Clouds of Sils Maria” and the heart-rending ghost story “Personal Shopper,” now in theaters — the director and his star have established the sort of rapport that suggests there could be more great work ahead.

amNewYork spoke with Assayas, 62, about his work with Stewart.

What, to you, makes Kristen such a great screen presence?

I think she’s incredibly gifted. I think also she has this completely fascinating relationship with the camera. It’s something beyond her own talents. She has it. It’s something that’s obvious. It’s something that struck me the first time I saw her onscreen in Sean Penn’s film, “Into the Wild.” She stands out. There is something that happens when she’s onscreen that’s beyond analyzing. What’s exciting about her is the mixture she has of animal instinct and deep technical knowledge of what she’s doing.

Do you encounter that much?

It’s very rare to have a combination of the two. You have great, very technical actresses, you have intuitive actresses, but actresses who have both, who know how to use their instinct to control in very nuanced ways what they do, it’s pretty unique.

What about for “Personal Shopper,” specifically?

In terms of a movie like this one, which deals with the supernatural, with the invisible, I thought it was really important to have an actress that’s as grounded and real as Kristen. The thing is, Kristen brings everything back to something very human, simple, obvious, and she connects that with the audience.

Are you guys going to work together again?

I would make another film with her tomorrow. I just don’t have the subject yet, but I’m sure I will find it. I think there’s really space for us to make another film. I would love it to happen.