Hi Ficbot,
I cannot comment on French, since I don't speak it. However, I read fluently in both English and Hebrew. I read a lot of both every day.
I never translate in my head. Translation is hard. Things that sound great in one language just don't work in another. You have to "think" in the language you're currently using, in my opinion. I'm equally comfortable with both languages I use, so it's like flipping a switch in my mind; I can be in one mode or the other.
I think as you continue to read in French, you'll get more used to it. You'll enter that "French" mode, and won't translate in your head.
Translation is rarely a one-for-one, word-for-word exercise. I took some translation classes, and have read several books in both Hebrew and English (the same books, translated from one language to the other). Some sentences that sound great in one language just don't work in the other, if translated word-for-word. Some similes won't work, some slang won't work, etc. Translation often requires mini rewrites, adapting the phrasing and wording to suit the new language.
So if you're reading in French, but translating it in your head to English, it might seem awkward. I think that after a while, you'll start "thinking" in French when you read it.
As for tenses... most people who use tenses daily don't really understand them! They just know how to use them, almost instinctively. It's like how you know to catch a ball thrown your way, without thinking about the physics involved.
Reading a LOT is key here. I moved to the US when I was thirteen, and reading in English was very difficult for me. When I'd read a novel in English, I always had a dictionary beside me. I'd fill up entire notebooks with words I didn't know, then look them up later. After about a hundred books, I only jotted down a handful of words a book. Another couple dozens of books, and reading in English was as natural as breathing.