To translate “heel over”, you’d use one of these two words ; gîte or bande. Bande would be used to talk about heel caused by an inside event (such as moving weight). Gîte would be used to talk about heel caused by an outside event (wind, for example). Gîte is used more often, even to talk about heel caused by an inside phenomenon.

Gîte is coming from the verb gîter, so you could easily say, for instance, that the boat is heeling over.

La bateau est en train de gîter

I’m not too sure about bande. But in my opinion, it’s useable that way as well.

"To hell over" would be best translated as gîter, which is a French verb to describe a boat which is tilting on a side:

(Marine) S’incliner sur un bord (en parlant d’un bateau), avoir de la gîte, de la bande.

You could also use incliner or pencher, even if those verbs are less specific and can be used for any tilting object. To describe the picture, you could then say:

Le bateau gîte.

Le bateau est penché.

Le bateau est incliné.

If it’s involuntary (effect of waves, wind, shift of cargo to one side, leak) it’s gîter or “donner de la bande”. If it’s done on purpose, to take part of the hull out of the water for repairs/cleanup it’s “caréner”.

If it’s over 90° and unvoluntary it is “chavirer” (or “dessaler” for dingies). When it’s voluntary (on a kayak) it’s “eskimauter”.