The islands were terra nullius when Dutch, British, French and Spanish ships discovered and settled them. Chile, not Argentina, was the closest country but no native Chilean or Argentine indigenous peoples even knew those islands existed. They'd never been settled by humans.
The Spanish Viceroyalty of the Río de la Plata was created in 1776; at the same time Spain acquired the French colony (Port St. Louis). So Spain took control over the French territory, and England retained its claim to its territory. This is the map from the year prior to the Viceroyalty being established.
