Butter — unsalted, and a lot of it. Cultured butter for finishing.
Dijon mustard, white and red wine vinegar, cornichons, capers.
Shallots, garlic, thyme, bay, parsley, tarragon, chervil.
Dry white wine, red wine, brandy, vermouth.
Crème fraîche, heavy cream, gruyère, comté.
Good stock — the single most French thing in any kitchen.