Aside from good old crafting and questing, here are other forms of activities that will allow you to earn gil in FFXIV. Leveling is important but you can do nothing in Eorzea without Gil.

Levequests
Many consider levequests a lot of fun to do. Not only are they a great opportunity to earn gil and other items that can be sold later on the market, but they also offer a variety of missions to complete. Every 12 hours, you can earn 3, up to a maximum of 100, levequests. As long as you speak to the appropriate levemete, every 5 levels, a levequest will unlock. You can typically talk to one in a main city once you unlock a levemete, and they will supply leves for the suitable level. Here are some tips on how you can earn gil this way:

Run battlecraft leves only.
The most opportunity for items to use or sell on the market can be found here. The other level are not so profitable although they also provide some rewards. The items are at battlecraft leves.

Pick a battlecraft leve that rewards items.
That item can be something that you can sell later on in the market although it's not something that you can use. Instead of potions or food, pick the level that rewards a piece of gear.

Hunt for treasure chests.
You may or may not come across a treasure chest while doing leves. Find item, potions, and other stuff by opening it. This helps increase your profit in some ways. Even if you are about to finish the level, try to search all areas.

Set max as difficulty level.
Ideally, you will receive a bonus if you finish the level with all objectives completed. Get more gil and experience by trying to kill any bounty targets as well.

Shun grand company leves.
In favor of giving you grand company seals, these will offer less rewards. You can bypass these leves as grand company seals are easy to get through other means.