Could you describe which part of the equipment of the street vendor is the "bac à frire"? A deep fryer is the container with the hot oil and usually a basket where the firites go and then the basket is lowered into the oil to cook. It can also refer to a stand alone machine for frying that you can use at home.
you're right.. I didn't think about the fact that hot dogs are steamed or boiled... (the person who asked me to translate this neither, in fact) so the word I need would be "the hot dog steamer", if this word exists...
Hot dog steamer it is, then! At least in NY.
I know that some sausages are grilled in other parts of the world, but not hot dogs in NYC, always steamed.
If the sausages are grilled, then I would simply call it a grill.