Jean-Baptiste mentions doves four times in the course of The Fall. Now, normally, talking about doves isn’t grounds for accusations of lunacy, but in this particular case, we have to doubt the man’s sanity. Why? Because he’s convinced that "the sky of Holland is filled with millions of doves, invisible because of their altitude, which flap their wings, rise or fall in unison, filling the heavenly space with dense multitudes of grayish feathers carried hither and thither by the wind."
And that’s only the first mention. The doves come up again later in Chapter Four, once briefly in Chapter Six, and most importantly at the end of the novel, when it begins snowing and Jean-Baptiste decides that the snow flakes are the doves, coming down to earth at last.
Before we discuss that might mean, let’s turn, as usual in this novel, to the Bible. In Christianity, the dove is the symbol of the holy spirit. It represents the divine grace of God, innocence, and purity. But remember that Jean-Baptiste defines grace as "irresponsibility." He doesn’t believe in God’s forgiveness. He doesn’t believe in divine intervention. He doesn’t think God is around anymore. After all, he is his own God, sitting enthroned in the "Dutch heaven" (that would be Mexico City) and judging all the pimps and thieves "below" him. As such, doves should have no place in his world.
Which is probably why the doves are restricted to the sky. They "would like to come down," he explains, "but there is […] never a head on which to light." In other words, there is no space for God here in Amsterdam. With that established, we can attack that juicy paragraph at the end of the novel where Jean-Baptiste thinks the falling snow is the doves coming to earth: "See the huge flakes drifting against the windowpanes. It must be the doves, surely. They finally make up their minds to come down, the little dears. […] Let’s hope they are bringing good news. Everyone will be saved, eh?"
That sure sounds hopeful. For a man so thoroughly convinced that God is dead, in a manner of speaking, it’s certainly odd for him to be talking about the holy spirit intervening to save mankind. Now read the next line from that passage: "You don’t believe it? Nor do I. But still I must go out."
Jean-Baptiste is trapped in a particularly awful scenario here. He can’t bring himself to have faith, to really believe that salvation is possible for mankind, but he also can’t bring himself to abandon hope entirely. In one sense, he "knows" that redemption isn’t coming, but in another sense, he desperately wishes it could. If you want to argue that Jean-Baptiste’s judge-penitent solution is false, this is probably a good place to start.