Well, despite being mounts, chocobos are birds after all, so avian terminology would apply I would think.

There are times during the main storyline when chocobo breeding is mentioned (especially during the Gridanian starting storyline), but I can't remember exactly what terminology was used to refer to male and females of the species, if any.

In past FF games, there wasn't any real specific terms used to differentiate gender - in FFVII for instance they were just called 'male chocobo' and 'female chocobo'. Young are naturally called chicks though (or 'chicobos' as they were mentioned in FFVIII ).