The boat, which survivors said had departed from Libya taking advantage of a respite in bad weather, was believed to be carrying some 170 people.
The Italian Coast Guard said those rescued, who included three children and 13 women, were brought to the port of Lampedusa.
Italian coastguard says it recovered bodies of 13 women, some of them pregnant, after a small overloaded boat carrying around 50 migrants capsized off Lampedusa.
The move comes after Spanish navy set sail in an attempt to save migrants stuck in the boat off the coast of Italy.
The French decision comes after the charity boat, which is currently in limbo off the coast of Italian island of Lampedusa, refused to take Spain's offer to dock citing an emergency situation.
The sailboat Alex, carrying 41 migrants, declined a Maltese offer to go to Malta, as the Mediterranea NGO operating it said such a long journey would have been dangerous for the people aboard.
Far-right League leader Matteo Salvini has tried to ban the Dutch-flagged vessel from approaching under a "closed ports" policy, which has seen migrants repeatedly stranded at sea.
Fishermen in the Tunisian town of Zarzis have been frontline actors in saving migrant lives at sea even though their humanitarian assistance is increasingly being compromised by hostile European migration policies.
The migrants, including 12 minors, were rescued on Monday off the coast of Libya by the Italian humanitarian group Mediterranea Saving Humans.
The worst of the refugee crises might be over, but migrants seeking a better life are finding new ways to Europe.
The refugees were rescued from 39 overcrowded boats including rubber dinghies some 20 nautical miles off the coast of Libya.
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