City had reached a verbal agreement with Alves more than a fortnight ago and had been so confident that he would be joining the club that they had already arranged media activities for him on their pre-season tour of the United States.
As late as Tuesday afternoon, City chiefs were still expecting the right-back to arrive in Manchester later this week, only to see him land in Paris to undergo a medical.
The French club's offer is almost double what City had agreed with Alves, who persuaded Juventus to cancel his contract by insisting he wanted to work with Pep Guardiola once again.
City were caught on the hop by Alves' decision and Guardiola, who dined with the Brazilian last Friday, is said to be livid at missing out on the player he coached at Barcelona.
Sources in France have suggested City made a last-ditch counter offer to Alves, matching what he would earn in Paris, though City officials insist they were unwilling to go anywhere near those figures and will now turn their attentions elsewhere.
City want to bring in four full-backs this summer and remain confident they will land Tottenham right-back Kyle Walker, as well as left-backs Benjamin Mendy, of Monaco, and Ryan Bertrand, of Southampton.
The Blues have been working hard to close a deal for Mendy over the past 10 days and are determined to have the France international in the squad for Monday's flight to the United States for pre-season.
City had been planning to sign Alves since April but will now have to find an alternative option for the second right-back role, having already scouted and discounted several options from across Europe.
Additional reporting by Loic Tanzi