Skyfarer is a free trpg set in the same universe as Fallen London. It's 21 pages with nice art, solid layout, and excellent graphic design. It also comes with Sky-Stories---a free supplement with additional npc, location, and event hooks---making this a total of 26 pages of professional material in an established universe at no cost to readers.
It's hard not to recommend it on that alone, but even if you're new to Fallen London or new to trpgs, this is an excellent entry point. The book leads with really good basic advice for getting started with a pen and paper rpgs, and the game is built to ensure that you never accidentally get rolling without a compelling adventuring hook in play.
Less information is provided on the Fallen London setting, so you may want to at least check out Sunless Skies first, but as long as your GM is a bit familiar with it, or as long as you agree as a group not to worry if one of you makes up a thing that contradicts canon, you should be fine. When in doubt, just kind of assume The Phantom Tollbooth but it's Dark Souls and also steampunk, and you'll be pointed in the right direction.
Mechanically, Skyfarer is pretty straightforward. You roll d10 against a target number (usually 6,) and add in small bonuses or penalties based on stats and effects. Failure means you take Peril, which builds up until you roll lower than it and get taken out of action. Roleplaying your character in a way that gets you into trouble builds up Tenacity, which can be used to buy down Peril, but also the GM is encouraged to just throw free heals at everyone every so often to keep the Peril accumulation from getting out of hand.
If you're used to the balance and gameflow in something like Fate or PbtA, you should be comfortable here.
One thing Skyfarer doesn't quite do is capture the way player language-learning works with the Fallen London games. In Sunless Sea, for example, when you're starting out, you're routinely asked to make decisions based on words and terms you don't have context for. As you play, you slowly learn what the terms mean, and you eventually start going on high alert when you hear a new word or an old word in a new context. In Skyfarer, the difficulty curve isn't tied in any way to learning the lore---which is probably for the best.
Another minor note is that Skyfarer goes through some weird hoops re: the captain of your flying train. The captain is a GMPC role, players can't play them, but they're also required by the rules to be out of commission, leaving important decision-making to the crew. This creates a weird dynamic, where the characters naturally want to look for guidance to someone who isn't allowed to give it, and I would strongly recommend either playing the crew as a captainless collective, allowing a player captain, or picking the "the captain is a collective hallucination" option to offset this.
Overall, though, Skyfarer is a solid, easy-to-learn game that's been dunked in the lore of Fallen London. If you're new to trpgs, or to non-d20 stuff, or if you like the Fallen London universe or simple, character-focused games, I would recommend both Skyfarer and the accompanying Sky-Stories supplement to you.
-Page 14, if a character with high peril succeeds a check but ends up in Danger anyway, does this cancel their success?