I'm not sure if there's a specific name for this particular combination, but as you mention it's specifically from a French restaurant, I'd call it a tartine, which is can refer to most anything served on a piece of bread or toast, cold or hot. If it were small enough to eaten in one bite, it'd be a canapé.
Growing up, we'd call a similar dish made with tuna salad (a mix of cooked tuna, mayo, onions, pickles) on bread and broiled 'til it developed a similar crust as a 'tuna boat' (to differentiate between a 'tuna melt' which had cheese on top), but I don't know that 'boat' in this context is generic enough to really convey any meaning to the typical person.
Because you mention cabbage, the topping in its uncooked form might be considered to be a cole slaw, which translates to cold salad but in the US generally means a cabbage salad dressed with vinaigrette or mayonnaise. Because of the ham and mayo, you might also call it a ham salad.
I'm not familiar with mayo-based cold salad recipes that use bread in them, but it's frequently used as a binder in crab cakes, which has some similarities as it's mayo-based and then broiled.
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This also looks like Centella asiatica or Indian pennywort, which is used as a culinary vegetable and as a medicinal herb.