French customs officers seized 2.2 tonnes of cocaine when they boarded the yacht Silandra on Wednesday evening following an international inquiry that lasted two years.
The drugs were worth an estimated 70 million euros, according to the head of the French West Indies anti-narcotic agency Octris, Simon Riondet.
The drugs were being destroyed as the authorities announced the seizure on Saturday, public prosecutor Eric Corbaux said.
Following an joint inquiry with their Spanish and British counterparts, the coastguard sent an airplane and two boats after the Silandra, finally stopping her about 200 kilometres off the coast of Martinique.
"The three suspects, who were on board on a 20-metre yacht, refused to cooperate," customs officer Michaël Lachaux told the AFP news agency. "We had to stop the boat at night on a raging sea."
The haul is the equivalent of a third of the total amount of cocaine seized by French customs in 2014 but not the largest ever - that was 4.3 tonnes seized on a Panamanian freighter off Martinique in 2006.
The two Spanish nationals were already known to the authorities in connection with the drugs trade.
One of them had been linked to "acts of terrorism" associated with the Basque separatist group Eta, according to Lachaux.
"It's a profile we come across from time to time, former terrorists who turn to smuggling."
The Caribbean is an important point of transit for cocaine produced in Peru, Colombia and Bolivia, about a third of which goes to Europe.
This week's operation was a result of European agencies' strategy of trying to intercept it in the region.