Errani, 38, had previously said it would be the last time she played singles at Roland Garros, and she eventually lost in the second round of qualifying.
She has completed the Tag-Team Grand Slam – winning each of the four majors – but now has her name six Grand Slam titles, including two of the French Open.
Errani also won the mixed doubles title with fellow compatriot Andrea Vavassori on Thursday.
“This is the best court in the world, and I have the best memories here, which is special to me,” Errani said.
“Sometimes you don’t like it 100% because you can’t stop and feel it, but now I feel it.
“I tried to realize what we were doing, and it was so big. Winning a Grand Slam is a big deal.”
The second seeds Errani and Paolini have not yet dropped a set on their way to the finals, but are taken away by Danilina and Krunic.
Errani and Paolini led 4-2 in the first set, but Danilina and Krunic hit it right, restoring equality with their own breakthrough in the fifth attempt.
The Italian ended a 55-minute match in Game 10 and broke the match in Game 10, suggesting another conventional victory could be on the card.
But Danilina and Krunic participated in the fight, gaining two breaks to join the board and force the decision-makers.
But the momentum was quickly dropped when Krunic and Danilina broke up in their first service match and Italian rivals competed to the finish line.
