Well, if Gilles de Rais didn't kill the children, who did?
Nobody did. There is no evidence to indicate that more children than might be expected went missing in his vicinity. The country was in a state of upheaval, with bands of soldiers living off the land, and the years when Gilles was supposedly pursuing his murderous career were a kind of mini Ice Age, with long and bitter winters. The attrition rate would have been high, especially among homeless beggars. Around forty children over eight years in a wide area would not have been an alarming or unusual number. A close examination of the evidence shows that children were going missing from areas he had no reason to visit, from Machecoul when he is recorded as living at Tiffauges, and that many of the children had no link to Gilles or his entourage at all. The attempt to explain this by positing the existence of two or more female procurers ranging the countryside is unconvincing, especially as none of Gilles' friends mentions them, not even Poitou and Henriet.
Further reading:
The Beast of Extermination: a numbers game
La Meffraye
So was it all a plot by the Church?
Now that the theory of Gilles' innocence has reached a wider audience, it is quite common for internet commentators to blame the Catholic Church. But this popular scapegoat was not responsible in his case, although the ecclesiastical court was certainly weaponised against him. His judge, Jean de Malestroit, was Bishop of Nantes but he plotted against Gilles in his capacity as Chancellor of Brittany. He was a lifelong Anglophile and felt that the Duchy would be more likely to keep its independence if it allied with England rather than with France. Ironically, in 1488 Brittany was handed over to French governance by the Lavals, Gilles' family.
The Church did not profit from Gilles' demise: his estates went to the sons of Jean V.
Further reading:
L'évêque diabolique - ?