Before. The 6th age of the Church, Reign of Mary, is the Church's triumphant resurrection from the persecutions/heresies of the 5th age (staring around the 1500s, with Martin Luther's protestantism). This period of peace has all nations as catholic and ruled by a catholic king and catholic popes. Many Church Fathers agree that this the 3rd and final "Holy Roman Empire".
This period will have the greatest Church council in history, with many saints, many religious and many conversions. It is said that Our Lady will destroy Protestantism, Muslims and all other sects, when those that survive WW3 will be forced to acknowledge that She is the one who gave the world peace. Only the jews will still remain (though many will convert).
After the death of the Great Monarch, peace slowly fades. His kingdom is divided and the catholics, forgetting the crisis of our times, give into sin and luxury. Then there is the "great falling away" where Scripture says 7 of the kings follow the anti-christ, and overcome the other 3 kings. Then the anti-christ reigns, most catholics apostasize, and the persecutions happen for 2.5 years. Enoch and Elias work miracles on earth, preach to the pagans and Jews and are killed. The anti-christ then is conquered.
This last peace of the earth, before the end of the world, will see ALL Jews finally convert, and there will be Christ's peace - his true and complete Kingship on earth. This peace won't last a "millenia" (this is protestant heresy) but it could be some decades; no one knows. Then the world will end.