I'm looking for some French readings (books, websites, anything goes) that are comprehensible enough so I wouldn't have to check every single word/grammatical construction. I'm fluent in English, and also Polish is my native language (Polish and French are grammatically quite similar, despite appearances), so I can get most of the text from context. Is there anything hard enough to actually learn something, but not so hard, that it would take me half an hour to go through a whole paragraph with full comprehension of what it says?
Given your grasp of French and English, you should make fast progress. I'd recommend starting with authors whose work you already know and like. These might include French and Polish authors whose work is available in both languages. If you prefer non-fiction, choose topics that will interest and motivate you.
Another strategy is to read works by members of the Academie Francaise. They tend to be well known by native French speakers. Reading them increases your cultural literacy. Translations, synopses, and commentaries are widely available for them.
My favorite author and academician is Marcel Pagnol. His language is both clear and expressive.
Let us know what you choose!
You don't mention how much French you actually speak beyond the similarity to Polish, so it's hard to recommend something specific.
This site has reading exercises by level, from A1 (beginner) to C1 (advanced). Most of the texts are excerpts from French books, so try out a few to see which level feels right, and then download the free ebook using the links at the bottom.