Gimp
Free and Open Source Software
If it's free and open source and it's also software, it can be discussed here. Subcommunity of Technology.
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GIMP opens each frame of the GIF as a layer. It's probably not a good choice for longer GIFs though.
I use normally just use EZGIF (an old-fashioned web tool), but I happen to also have Adobe Fireworks CS4 (which is from 2008) on an old MacBook for more advanced editing.
There's probably a good FOSS tool out there, but I don't edit or even create GIFs often enough to bother looking.
Imagemagick + ecosia/google
ScreenToGif
To make brand new gifs: DaVinci Resolve, because it is super easy to add captions, and then convert to gif with ffmpeg. To modify existing gifs: GIMP
I haven't found any FOSS programs specifically for editing GIFs, so I'd like to know too. Kdenlive and GIMP can import and export them, but they're definitely not designed for this purpose, the former being more of a typical video editor which seems to have no awareness of the loop points of GIFs, and the latter being a photo editor that imports the difference between every frame as a separate layer, making editing very awkward.
ezgif.com works for this purpose, but I don't think it is FOSS.