Yes, Trello desktop is indeed free! You can download it from the official website to use on Windows, Mac and Linux, with no fees or subscriptions.
Trello Desktop gives you many of the same features that are available through the web version, but with access to the fullest power of the desktop. This includes faster speed and performance, the ability to work offline, notifications, history, and more.
Trello also provides a range of features and integrations via Power-Ups – like calendar, map views, real-time data, and file attachments. A subscription to a Power-Up pack can unlock greater functionality, but using the basic version is still free.
Here's the link to the download page: https://trello.com/platforms
I hope this helped answer your question. Let me know if you have any follow-up questions!