Errani, 38, previously said this would be her last time playing singles at Roland Garros and she ultimately lost in the second round of qualifying.
She had already completed the career Golden Slam in doubles – winning each of the four majors and Olympic gold – but now boasts six Grand Slam titles to her name, including two at the French Open.
Errani also won the mixed doubles title alongside compatriot Andrea Vavassori on Thursday.
“This is the best court in the world, I have the best memories here and it’s so special for me,” Errani said.
“Sometimes you are not enjoying it 100% because you can’t stop and feel it, but right now I’m feeling it.
“I’m trying to realise what we are doing and it’s so big. Winning a Grand Slam is such a big thing.”
Second seeds Errani and Paolini had not dropped a set en route to the final but were taken the distance by Danilina and Krunic.
Errani and Paolini broke for a 4-2 lead in the first set but Danilina and Krunic hit straight back, restoring parity with a break of their own at the fifth attempt.
The Italians wrapped up a 55-minute set with a break of serve in the 10th game, signalling another routine victory could be on the cards.
But Danilina and Krunic came out fighting, earning two breaks to get on the board and force a decider.
That momentum was quickly wrested away, though, when Krunic and Danilina were each broken on their first service games and their Italian rivals raced to the finish line.