The Chipolopolo beat the Ivory Coast 8-7 on penalties after a goalless final on Sunday night in Libreville - the scene of a plane crash 19 years ago, en route to a World Cup qualifier against Senegal, which defines the country's modern footballing history.
The Zambia national team's plane crashed into the sea shortly after a refuelling stop, killing 18 players - Efford Chabala, Richard Mwanza, John Soko, Whiteson Changwe, Robert Watyakeni, Estone Mulenga, Derby Makinka, Moses Chikwalakwala, Wisdom Chansa, Kelvin Mutale, Timothy Mwitwa, Numba Mwila, Samuel Chomba, Moses Masuwa, Kenani Simambe, Godfrey Kangwa, Winter Mumba and Patrick Banda - along with Zambian Football Association president Michael Mwape and coaches Godfrey Chitalu and Alex Chola.
Star player Kalusha only survived as he had travelled separately from Holland, where he was playing for PSV Eindhoven. Now the Zambian FA president, Kalusha joined the current squad as they paid tribute in a ceremony on the Beach Sabliere ahead of the final.
Renard told ESPN after Saturday's poignant triumph: "Kalusha was one of the best Zambian players of the last century. Then he was coach of the national team, now our president.
"He survived the crash - he was supposed to have been on that plane which was going to play a World Cup qualifier against Senegal. He knows how terrible this crash was for the nation. I want to dedicate this title to him."
He added: "We wanted to honour the dead players and that strengthened us.
"Our first game (in this year's tournament) was against Senegal and the team was on its way to Senegal for a match when the plane crashed. The plane crashed in Gabon and we won the final in Gabon.
"It was a sign of destiny, written in the sky. There was a force with us. I think God has helped us and given us strength."
It was Zambia's first Nations Cup title and their third final, including in 1994 when Kalusha led a makeshift squad to within one hurdle of glory.
"I said to the players that a team of 'replacements' took Zambia to the final in 1994, so why not us?" said Renard. "We always believed and said this was our time.
"Winning on penalties is perhaps not the best way, but we cannot complain. It is cruel for the Ivory Coast, but we deserved it.
"We will savour this moment, we have made a permanent mark on Zambian football history."
Zambia needed two opportunities to seal victory in the shoot-out, with Rainford Kalaba failing to capitalise on Kolo Toure's miss before Stophira Sunzu punished Gervinho's wayward spot-kick.
"(My penalty) was supposed to be the winning goal," Kalaba said on the Zambian FA's website. "These things happen in football, but then you have to move on.
"You just have to forget about the past and concentrate on the future."
That he did, as he enjoyed his team's emotional celebrations.
"We wanted to honour the players that died here, so that the families of the deceased players can feel much better and I am pleased we achieved that," he said. "I have been dreaming about this wonderful moment."
The Elephants had the better of the chances in normal time, with Didier Drogba missing from the spot and Yaya Toure and Max Gradel going close.
And coach Francois Zahoui said: "We had chances to score and we didn't take them. We did not know how to kill off the match and Zambia took confidence from that.
"We knew it would be a difficult final, Zambia wanted the trophy like us and they were not there by chance."
Goalkeeper Boubacar Barry added: "It's disappointing but it's not the end of the world. We finished as the best defense and the best attack, so it's frustrating, but we must learn the lessons of this tournament."