It looks like bans for odd/even license plates were used in Paris in 2014 [1] and 1997 [2], but not before then. However, a similar scheme was used to ration gasoline in the US during the 70s [3].

The only source I can find for the claim about police confusion is the one cited by Wikipedia [4], whose reliability I'm inclined to doubt based on the 1997/1977 discrepancy.

[1] https://www.npr.org/sections/thetwo-way/2014/03/17/290849704...

[2] https://www.wired.com/1997/09/paris-smog/

[3] https://www.npr.org/sections/pictureshow/2012/11/10/16479229...

[4] https://en.m.wikipedia.org/wiki/Odd%E2%80%93even_rationing#D...