Dear Harry, in Serre's collected papers, vol.1, page 183 [or Annals of Math.58(1953) page 270] you'll find (line -5)

"Soit $\mathcal C$ une classe vérifiant (II_A)..."

and many such examples on the same page, corroborating your testimony on papers and books you read in French. I recoil in horror at the thought that some heretic might not consider this a sufficient proof that the usage of "vérifie" in the sense "satisfies" is more than acceptable in French. And now for the kill: Bourbaki, in Topologie Générale, Chapitre 1, §6, page 61 (line -15)[Quatrième édition] writes

"Pour qu'un ensemble de parties satisfaisant à (F_1) vérifie aussi..."

What does our hypothetical miscreant say now?

Dear Harry, in Serre's collected papers, vol.1, page 183 [or Annals of Math.58(1953) page 270] you'll find (line -5)

"Soit $\mathcal C$ une classe vérifiant (II_A)..."

and many such examples on the same page, corroborating your testimony on papers and books you read in French. I recoil in horror at the thought that some heretic might not consider this a sufficient proof that the usage of "vérifie" in the sense "satisfies" is more than acceptable in French. Another quote: Bourbaki, in Topologie Générale, Chapitre 1, §6, page 61 (line -15)[Quatrième édition] writes

"Pour qu'un ensemble de parties satisfaisant à (F_1) vérifie aussi..."