The Final Fantasy series has featured numerous iterations of a character class system. One was originally planned for Final Fantasy 7, but it was cut before release. FF7 went through a number of different ideas during development, including a New York City setting and Aerith and Sephiroth being siblings.
The first Final Fantasy game used a character class system, with six jobs available for the four player characters. If the player completed a quest involving Bahamut, the jobs were upgraded to more advanced classes. These jobs formed the basis for character class systems in other Final Fantasy games, most notably FF5 and Final Fantasy Tactics. Even some of the games that abandoned the job system used variations of its abilities, like the Guardian Force/Command system from FF8 and the Sphere Grid from FF10. Still, the job system changes depending on the needs of the game; the action-RPG gameplay of FF15 didn't need too many abilities and commands, so there was no need for jobs, whereas the multiple players and roles in FFXIV requires lots of jobs.
FF7 replaced the job system with materia. All the commands associated with classes could instead be equipped via materia found in the game, like the Thief job's Steal ability or the Knight/Paladin's Cover ability. All characters had free access to spells, so long as they had the correct materia. But it turns out FF7's characters were planned to have defined jobs, but they were phased out.
The Potential Job Classes Of FF7's Avalanche Characters
The Final Fantasy 7 Ultimania Guide (translated by The Lifestream) features FF7 concept art and planning documents for the game's playable characters. All the cast members of FF7 were originally going to have their own jobs. Cloud Strife was a Mystic Knight, Barret Wallace was a Gunner, Tifa Lockheart was a Shooter (as in, a UFC-style mixed martial artist), Aerith Gainsborough was a Geomancer, Red XIII was a Beast, Cait Sith a Toysaurus/Beastmaster, Yuffie Kisaragi was a Ninja/Assassin, Cid Highwind was a Dragoon, and Vincent Valentine was a Horror-Terror/Horror-Researcher.
It's possible these jobs were going to exist in name only or act as explanations for the Limit Breaks possessed by each character. The Japanese version of FF6 also had job names on the menu screen, after all, but they couldn't be switched. The reason classes were cut from FF7 could have been to remove any confusion about its gameplay system, as developers likely didn't want fans to think switchable jobs were returning. Final Fantasy 7 was meant to represent a new era for the series, and the addition of job names might have connected the game too closely with older Final Fantasy titles.
Source: The Lifestream, (2), (3)