Jean Luc Picard had been taken by the Borg and transformed into their spokes-borg Locutus. However after his recovery all the Borg implants and Borg nano-machines were removed.
Though his implants were removed and his wounds were allowed to heal, Picard's assimilation continued to haunt him. He returned to Earth, paying a visit to his family in La Barre, France, where he eventually came to terms with the ordeal. (TNG: "Family") Memory Alpha -> Locutus of Borg
In the second clash, it was not Borg implants which gave Picard an edge, but a memory of the Borg systems which allowed him to create an effective strategy against them.
When the Borg attempted a second invasion in 2373, Picard's experience with the Borg not only gave him prior warning of the attack, but also allowed him to pinpoint a weakness in the Borg defenses, resulting in the fleet destroying the invading vessel. (Star Trek: First Contact)
The interaction between Jean Luc Picard and the Borg was a two-way transfer of information, the Borg gained valuable information about the Federation and its defense structure, ship capacities and ally information. What Jean Luc knew, the Borg knew. But the Borg share information fairly evenly so even Borg who have never met Locutus, know of him. This transfer of information also meant Jean Luc was privy to information about the Borg no human would know without direct experience (e.g. Seven of Nine).