Le Cerf Volant, a 14-gun warship, was probably captured in late December 1668 (New Style date) by Edward Collier while commanding the Oxford. Collier seized the French ship at Cow island while it was anchored not far from Morgan's ship.
According to Dudley Pope in Harry Morgan's Way: The Biography Of Sir Henry Morgan 1635-1688 (2013), Sir Thomas Modyford, governor of Jamaica, gave Edward Collier command of the Oxford and ordered him to follow up on a complaint that Le Cerf Volant was a pirate. After this, Collier was to join Henry Morgan, who had been given the rank of admiral in January 1668 with orders "to take action against the Spanish". According to Pope,
Collier guessed that he could carry out both orders at Cow Island
because Morgan was there and the French ship had probably joined him...
As the Oxford sailed into the Cow Island anchorage and fired a salute
to Morgan (who was seeing the frigate for the first time), Collier
sighted Le Cerf Volant anchored nearby….
Following the arrest of the French captain and his crew, Collier
brought into Port Royal the captain and forty-five-man crew of Le Cerf
Volant (fourteen guns) of La Rochelle, clapped in irons and accused of
plundering a Virginia merchantman. Sir James Modyford, the governor’s
brother, had no difficulty in condemning the unfortunate French
master, although he was later reprieved, and his ship was condemned as
a lawful prize.
Source: Jon Latimer, 'Buccaneers of the Caribbean: How Piracy Forged an Empire' (2009)
Renamed Satisfaction, the newly acquired ship and the Oxford sailed back to Cow Island for a rendezvous with Morgan. The Oxford blew up shortly after, on January 12th (New Style), when the powder magazine was ignited by a spark. Morgan and Collier, who were on board at the time, survived but around 200 others perished.
The exact date is hard to pin down but, according to Pirates of the Americas by David F. Marley, Collier left Port Royal (Jamaica) for Cow Island (Haiti) on Dec 20th (this appears to be a New Style date, so Dec 10th old style) and the Oxford blew up on Jan 12th (Jan 2nd old style) after returning, again from Port Royal. This makes a late December (New Style) date most likely for the seizure of Le Cerf Volant.