Pont Neuf potatoes are basically squat, somewhat thick-cut French fries.
They should be soft, fluffy and hot inside, and never so crispy that they shatter in all directions when you try to stick your fork in them.
You want to use very floury potatoes, and preferably ones that have been in storage for a while to develop even more starch and get more floury.
In general, the size of each Pont Neuf French fry is 1/3 inch thick x 2 1/2 to 3 inches long (1 cm thick x 7 to 8 cm long.)
Peel potatoes, then slice. Discard any rounded, uneven pieces leftover.
Wash the potato pieces to get excess starch of them, then pat them dry.
Heat oil to 300 F / 150 C (to test, a fry put in it should rise slowly to the surface covered in small bubbles.)
Cook by handfuls, allowing each handful 6 to 7 minutes. They won’t brown during this first cooking stage.
When all the handfuls are cooked, raise the oil temperature to 350 F / 180 C, put all the Fries back in at once into the oil for a further 4 to 5 minutes until golden.
Drain on absorbent paper, sprinkle with fine salt, serve.
The story goes that the first place in Paris with the facilities to deep-fry potatoes in a lot of oil was near the Pont Neuf (new bridge.)