"sauce piquante", although this traditional term also includes mustard and horseradish sauces, from before the hot pepper was discovered.
"sauce au piment rouge" (red pepper sauce) would probably be better for the hot sauces such as habanero sauces.
The name for the sauce is spelled remoulade (French rémoulade).
chaud
"hot peppers" is "piment" (or "piments" for plural) in French.
The sun is hot in french: Le soleil est chaud
chaud(e)
It's "tomato" in English. It's "tomate" in French.
tube chaud
vous êtes chaud
Fondue
il fait chaud
The French sauce (behr-nayz) is spelled Béarnaise sauce - but it is not used on Eggs Benedict (which has Hollandaise sauce); it is used on the similar dish Eggs Provençal.
Sauce is correct.