After submitting their candidacies for posts including deacon, priest and bishop, the women attended a mass at the Madeleine church in central Paris to mark the feast of Saint Mary Magdalene.
Their campaign echoes a quest by Anne Soupa, a 73-year-old activist theologian, who in May declared herself a candidate to lead the archdiocese of Lyon.
That post has been vacant since Cardinal Philippe Barbarin stepped down last year over a paedophilia scandal involving one of his priests.
"The Church is experiencing a deep crisis, and we need to open up its doors," said Soupa, who accompanied the women to Paris.
Toutes apôtres ! pic.twitter.com/eWS58BSxsS
— Toutes Apôtres ! (@ToutesApotres) July 22, 2020
The Catholic Church makes women invisible
"Women are rendered invisible in the Catholic Church," she said. "In this age of equality, when women's abilities are recognised by all, we can't continue like this."
Scores of paedophilia and sexual abuse charges have rocked the Church worldwide in recent years, prompting calls for wholesale change from critics who say the organisation has failed to adapt its traditions to the demands of the modern world.
So far Pope Francis, the global leader of the Catholic Church, who backs many progressive causes such as allowing priests to marry, has refused calls to give women a greater role -- let alone allow them to be ordained.
Last year, he declined to move forward on letting women become deacons, an ordained position just below that of priest, which proponents say could help fill the gap in countries were priest numbers are dwindling.
"This isn't a move against the Church, but for it," Soupa insisted.
