How do you make a movie about a heart transplant and not make it a medical drama?

Katell Quillevere’s “Heal the Living,” out on Blu-ray from Kino Lorber, achieves this by giving equal weight to the donor and to the recipient as well as the doctors. The result is a humane triptych of a film which, although it lacks real suspense or drama, contains moments of stunning beauty and enveloping empathy.

At one end of the chain is a teenager, Simon (Gabin Verbet), sneaking out of his girlfriend’s bedroom late at night for an early morning surfing trip with his buddies. The wordless surfing scenes, with Simon enveloped in a slowly unfolding universe of blues and greens as Alexandre Desplat’s score swells on the soundtrack, are gorgeous and otherworldly.

At the other end is Claire (Anne Dorval), a former musician with a weak heart who has two college-age sons and a lover doting on her. Claire puts on a brave face to her family, but her fragility and her fear shine through, and her sons care for her as if they were her parents.

In the middle are the doctors, whose efforts will connect Simon and Claire. Quillevere eschews E.R. theatrics for a methodical, fascinating look at how organ transplants are carried out – the procedures, the phone calls, the incisions. Instead of demystifying the procedure, it somehow makes transplant operation seem even more miraculous. First the fist-sized organ is powering one life; then it is powering another.

But in the midst of such a clinical approach, Quillevere finds space for small grace notes of humanity among the doctors, such as one middle-aged surgeon listening to an inappropriate pop song on the way to work, or another (Tahir Salam of “A Prophet”) stopping the procedure to perform an extraordinary act of empathy that left me reeling.

It was those little moments along the way that kept me going when “Heal the Living” got a little overly meditative. That and the beauty of the images, and Desplat’s score, and the movie’s embrace of the triumphs and tragedies of life.

As one family in the film experiences the worst day of their lives, another experiences their best. And one couldn’t happen without the other.