She was the first female lawyer to pass the Guadeloupe Bar and the second black woman elected to the French National Assembly, shortly after Eugénie Éboué-Tell.

Archimède was a lawyer, prominent member of the Parti Communiste Guadeloupeen (PCG), founder and president of the Union des Femmes Guadeloupeennes, conseiller general from Basse-Terre, Guadeloupe.

In 1952, she returned to the bar in Guadeloupe, then is elected in 1953 as Deputy of Basse-Terre Mayor, Elie Chauferain, whilst continuing her activity as a lawyer, until she replaced him in 1956.

She contributed actively to the transformation of the UFF federation into the Union of Guadeloupean Women ("Union des Femmes Guadeloupéennes" in French) In August 1969 she met Angela Davis, after arriving in Basse-Terre from Cuba by boat Davis and her friends have been arrested by French customs officers and had their passport confiscated.

On 14 January 2011, during the inauguration of a new amphitheater at the UAG in the city of Saint-Claude, the jury reveals the results after a referendum announcing Gerty Archimède will be the Caribbean personality the building will be named after.