Classique is likely based on the defunct Oldsmobile ("classic" being a play on "old"), as the Stallion from GTA IV has a lot of influence from Oldsmobiles. The logo is somewhat based on the Saturn Corporation logo (also somewhat similar to the Oldsmobile logo), but the border is a circle and the center has a loop that mimics the first C in "Classique" from the Stallion's grille. The logo of Classique clearly features a male sperm fertilising a female egg.
There is a vehicle brand logo and police dispatch identification voice file located among the on-disc GTA V files, suggesting an early planned use for the Stallion and/or Classique. However, with the Stallion now branded as Declasse, these files continue to be unused.
In GTA IV, the police refer to the Declasse Sabre GT as a "Classique Sabre GT", likely owing to its Oldsmobile design influence.