Batflat - Lightweight, fast, easy, and free CMS.
Bludit - Bludit is a web application to build your own website or blog in seconds, it's completely free and open source. Markdown support.
Grav - The modern open source flat-file CMS
WordPress - WordPress is web software you can use to create a beautiful website or blog. We like to say that WordPress is both free and priceless at the same time.
HTMLy - HTMLy is an open source databaseless blogging platform. A Flat-File Blog and Flat-File CMS written in PHP prioritizes simplicity and speed.
Fansoro - Fansoro is a Modern Open Source Flat-File Content Management System.