Well, I have learned about coordinating and subordinating conjunctions at school, but only in French. I don't think (that) I've ever learned anything about them in English because the last time I had a class, I hadn't reached that level yet. So it just means (that) French and English have a lot in common, after all!

A lot of what I know of French is useful in English. Sometimes I'll spot mistakes from native English speakers, and those are mistakes I wouldn't make because I understand the rule behind it from my knoweldge of French. But of course, on the other hand, I'm also making different mistakes, and I suppose (that) those are often the kind of mistakes that native English speakers would never make!

I found
this link, among others, about conjunctions. So "that" is a subordinating conjunction, just as its French equivalent "que" is, but in French it's impossible to omit this word, which is why I'm so confused. I've read a few links I found through Google, but I couldn't find any answer to my question yet. Fafner's answer seems plausible, but then it still leaves me wondering is one is formal and the other isn't.
You don't have any idea on this, jeffbert?