First contact between Klingons and the Federation as told in the episode "First Contact". Totally different to what we saw in "Broken Bow" (or even "The Vulcan Hello"), this version led to decades of war and the creation of the Prime Directive.
First contact with Klingons yes, but did Picard say it was between Klingons and Humans? The Federation has many species as members.
I thought the logical conclusion to make from canonical evidence in summary is that Picard was referring to Vulcan-Klingon first contact. After all, Picard is a Federation citizen, and Vulcan history has influenced Federation policy, has it not?