Unlike other Christian thinkers of our time, Jacques Maritain did not renounce the concept of Christendom. But he had the skill to apply to it a scholastic notion full of potential: that of analogy. It is legitimate to aspire to a new Christendom, yes, but not identical to the one that once existed (which Maritain, for convenience, identifies with the Holy Roman Empire), but analogous.
This means that Christ will continue to inspire the actions of rulers and citizens, but not through a political power whose mission is to serve the Truth, rather through the personal conduct of each Christian. That, in summary.
Then Maritain goes on to outline some features of this future Christendom, in what is perhaps the most debatable part of the book. Indeed, the author catches a glimpse of the concept of secularity as we know it today, but I don't believe he fully embraces all its implications. For one of them is precisely that the polis should be organized according to each person's free reasoning, without concrete directives issued by the Church in matters unrelated to the Catechism.