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..."