The French sauce made from shallots, white wine, vinegar, and butter is beurre blanc.
Beurre blanc is a warm emulsified butter sauce. Finely chopped shallots are reduced with white wine and vinegar, then cold butter is gradually whisked in so the fat and liquid remain combined as a creamy sauce.
The sauce is strongly associated with the Loire region and Nantes, where it is also called beurre Nantais. A popular origin story credits cook Clémence Lefeuvre around the turn of the 20th century, though different accounts disagree about exactly where and how she created it.
Beurre blanc is classically served with pike and other fish, but it also accompanies vegetables and eggs. It contains no egg yolks, unlike hollandaise and béarnaise. Velouté is different again: it is a roux-thickened sauce made from stock, not a butter emulsion.