Prepare the fries first. Rinse cut potatoes in cold water until water runs clear to remove surface starch, then pat dry with a clean towel.
Heat oil to 150 C (300 F). Blanche fries in batches for 4-5 minutes until soft but not colored. Drain on a rack; they should feel tender inside and pale outside.
Increase oil temperature to 190 C (375 F). Fry blanched potatoes in batches for 2-3 minutes until deeply golden and crisp. Drain on paper and season immediately with salt.
While fries rest, clean mussels. Discard any with cracked shells or that stay open when tapped. Rinse under cold water to remove grit and trim beards.
In a large pot over medium heat, melt butter and add shallot and garlic. Sauté 1-2 minutes until translucent and fragrant, with a faint sweet aroma from the shallot.
Pour in white wine and bring to a rolling simmer. Let alcohol evaporate and liquid reduce slightly for 2-3 minutes so the broth concentrates flavors.
Add mussels, cover, and steam for 4-6 minutes, shaking the pot once, until most mussels are open. You should hear a lively hiss and smell briny, aromatic steam.
Remove pot from heat, stir in chopped parsley and a grind of black pepper. Discard any mussels that remain tightly closed.
Serve immediately with a bowl of mussels and their broth alongside a mound of hot fries. Dip fries into the broth or spoon mussels over fries for a balanced bite of brine and crunch.