The long-planned trip to Rome, which includes talks with Italian Prime Minister Mario Draghi, follows the publication of a devastating report estimating that French Catholic clergy had abused 216,000 children since 1950.
Pope Francis, who has made battling the global scourge of clerical abuse a priority of his papacy, expressed "my shame, our shame" at the findings, echoing a similar sentiment from French church leaders.
But a row broke out when Archbishop Eric de Moulins-Beaufort, the head of the Bishops' Conference of France, said priests were not obliged to report sexual abuse if they heard about it during the Catholic ritual of confession, used to admit to sins.
His words were in line with Vatican guidelines updated last year, which call on clerics to report claims of abuse. They say confession is subject to "the strictest bond of the sacramental seal", while saying the confessor should try and convince the penitent to tell someone else.
In France, victims' advocates pointed out that French law recognises professional confidentiality for priests, but it does not apply in potentially criminal cases involving violence or sexual assault against minors.
Moulins-Beaufort was called to a meeting with Interior Minister Gerald Darmanin, and later insisted that protecting children was "an absolute priority".
Darmanin accompanied Castex and French Foreign Minister Jean-Yves Le Drian to the Vatican, in the visit marking 100 years since the reestablishment of diplomatic relations between France and the Holy See (Source: FRANCE 24).