The most relevant Quatrain I could find was the one I have given below. In this Quatrain Nostradamus indicates that he visualized events 7 thousand years after 20 years of the Moon’s reign. He only indicates that the events which he prophesied for those 7 thousand years will be fulfilled; there is no talk of the world ending after that.
Which ever way one dates the 20 years of the Moon’s reign; from the time the Prophecies of Nostradamus were first published or at some later date, one thing is sure the world is not going to end at least for the next 7 thousand years; give and take a few hundred years.
Century 1 - 48
Vingt ans du regne de la Lune passez,
Sept mil ans autre tiendra sa Monarchie :
Quand le Soleil prendra ses iours lassez,
Lors accomplit & mine ma prophetie.
When twenty years of the Moon's reign have passed another will take up his rule for seven thousand years. When the Sun takes up the next cycle then my prophecy and warning will be accomplished.