Portland Trailblazers star Nicolas Batum collected 17 points and six rebounds while Boris Diaw had 15 points and his San Antonio Spurs teammate Tony Parker added 12 points for France, who lost to Spain in the 2011 final.
"It's great for French basketball, for the former players, my family, friends. This is for all of France, for all sport," gushed Parker.
"It's incredible to be the first French team to win the title."
It was a huge relief for France who had failed to take the title after 13 previous top-four finishes didn't produce a crown.
Lithuania were hoping to finally claim a fourth European crown after titles in 1937, 1939 and 2003.
But the Baltic side will have to be happy with a second silver after 1995.
Linas Kleiza tallied 20 points while Mantas Kalnietis scored 19 for Lithuania.
Batum scored 10 points in the second quarter and led the decisive 21-3 French run to close the first half — effectively taking control of the game with a 50-34 lead at half-time.
Lithuania were able to cut the deficit to 14 points early in the third quarter and late in the fourth, but France would not allow them any closer.
The French dethroned two-time reigning champions Spain in the semi-finals, but the Spanish bounced back to take the bronze medal by knocking off Croatia 92-66.
Sergio Llull scored 21 points while Marc Gasol collected 17 points, eight rebounds and two assists and Victor Claver totalled 16 points.
"We were very disappointed about losing the semi-final against France. Our goal was to take a medal from this tournament. This was our chance. We showed that we are a winning team," said Claver.
The Spanish have won a medal at seven of the last eight European championships, taking gold in 2009 and 2011; silver in 1999, 2003 and 2007; and bronze in 2001.