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I'm not sure what editing software Fontaine uses exactly (I'm guessing it's one of Premiere, Resolve or Final Cut Pro), but editing software itself contributes little to the overall style of the video (or at least, it shouldn't). It's the style of the director of the video that you like, not the editing software. Editing software is just a tool and even if you happened to use the exact same editing software as them, your video wouldn't look like theirs because you are a different person with your own style and flair.
If you want to get into editing, I'd suggest starting with beginner apps like Filmora (the free version) on phone. I have personal experience with that app, and you can get a lot of work done on it. Then you can move on to the bigger and expensive software later on, but be aware that they have a learning curve. You'd be surprised how many brilliant editing applications are available for free (with a simple UI) anyways. Look on You Tube for Justin Brown's lists of great editing software (lists are available for PC, Mac, iOS and Android).
TLDR; I don't know, but the software isn't responsible for the style.
Super agree with MohanaMisra. I think that if it is possible to tell which software someone uses then there's something wrong with the editor(not the software but the person that edits). Or maybe it is a lazy commercial edit. When a professional does the editing, and does it with all the seriousness, you wouldn't be able to tell what is used. And since you asked it I guess you want to edit yourself, and I will recommend this simple software https://www.movavi.com/videoeditor/