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.
France is prepared to take in 40 migrants who fulfill the criteria for gaining refugee status from the Spanish Open Arms rescue vessel, the French interior ministry said on Sunday.
The migrants must be "in need of protection", the ministry said in a statement.
Earlier, the rescue ship carrying more than a hundred migrants off the coast of Italy said that it could not accept an offer from Spain to dock in Algeciras, citing an emergency situation onboard.
The migrants, most of whom are African, were picked up by the Open Arms boat off the coast of Libya and have been waiting to disembark on the southern Italian island of Lampedusa.
"We do not accept Spain as a port to go because we are in a state of extreme humanitarian emergency. What they need is to be disembarked now," Open Arms' spokeswoman said.
"It is unthinkable to navigate for six days; that is what it would takes for us to arrive to Algeciras."
Spain's government offered to take in the charity vessel because of Italy's "inconceivable" refusal to allow it to dock.
Prime Minister Pedro Sanchez "today ordered the port of Algeciras to be ready to receive the boat Open Arms," which is currently in limbo off the Italian island of Lampedusa, his office said in a statement.
It cited the "urgent situation" on the vessel and the "inconceivable decision by the Italian authorities ... to close all its ports" to the migrants.
The Open Arms organisation said Madrid had taken the decision because of the "untenable" situation for the 105 migrants still aboard, including two children.
"Spanish ports are not the closest or the safest for Open Arms ... but for now Spain is the only country willing to accept it," the organisation said.
Italy's far-right Interior Minister Matteo Salvini, who is also deputy prime minister, has refused to allow migrant rescue vessels to dock as part of his hardline policies.
Italy's government on Saturday reluctantly agreed to let 27 migrant children from the Proactiva Open Arms disembark though it demanded that the rest stay aboard.