The Croque-Hawaïen is the French café's pineapple-on-pizza, a Croque-Monsieur with a slice of canned or grilled pineapple tucked between the ham and the cheese before the whole sandwich goes under the broiler. The build is otherwise the classique: pain de mie, jambon de Paris, Gruyère or Emmental, béchamel, blistered top. The pineapple is the entire argument. Under the heat it softens, browns at the edges, and releases enough liquid to thin the béchamel slightly. The acid of the fruit cuts the salt of the ham and the fat of the cheese, and what should not work, by most rules of French café cooking, in fact works, which is the irritation. A faction of café cooks regard the variant as a small betrayal of the format. The diners who order it generally do not care.
The structural logic, once a kitchen accepts it, is identical to the standard ham-and-cheese-and-pineapple combination familiar from Hawaiian pizza, with the only adjustment being that the heat of the broiler is more aggressive than a pizza oven and the pineapple has less time to lose its water. Most cafés use canned pineapple rings rather than fresh, which sit flat against the ham, give up moisture in a controlled way, and arrive on the plate already in their final form. A fresh-pineapple version is possible but rare. The acid behaves differently when fresh, and the resulting sandwich can taste raw in a way the canned version does not. The drink with it is generally a beer rather than a wine, on the same logic that governs Hawaiian pizza.
The variant is part of a small French tradition of borrowing tropical-island shorthand for menu items that include pineapple, the hawaïen tag attaching to pizzas, salads, and various skewers wherever the fruit shows up. The Croque-Hawaïen is the sandwich-shaped end of that lineage. The full cluster of croque variants is mapped at Croque-Monsieur, where it sits alongside Norvégien, Provençal, Savoyard, and the other named bends. The Hawaïen is the most contested of them, which is also why it is one of the most ordered.