For the mussels: In a large pot on medium heat, add the olive oil and chorizo. Break up the chorizo while cooking to create fine crumbles. Season with a nice pinch of salt and ground pepper and cook, stirring, until the bits and pieces are crisp, 5 to 8 minutes.
Add the wine, bring to a simmer and simmer for a few minutes. Stir in the cream. Immediately add the mussels and cover the pot with a lid. Jiggle the pot a bit to coat with the liquid on the bottom. Steam until most of the mussels are opened, about 5 minutes. Discard ones that do not open in the steaming process.
For the fries: Fry the shoestring French fries according to the package instructions.
Add the oil, garlic and a few grinds of pepper to a large bowl. Mix and mash to combine. Add the hot fries to the bowl and toss while sprinkling with the parsley. Serve with mayonnaise for dipping.
Sprinkle the mussels with the cilantro and serve with the fries.