Meaning "I write" and "I'm writing" are both translated the same, for example: escribo, j'ecris, يكتب.
I can't speak French, but you can certainly say "estoy escribiendo", in Spanish if you mean you are writing right now. Similarly, you can say "أنا كاتب" in Fusha Arabic, which is usually translated as "I'm writing", although it is not exactly the same, because it could also mean "I'm a writer". In addition, there are some forms in dialects to express that idea, for example in Moroccan Darija you could say "كنكتب" (I'm writing) in contrast to "نكتب" (I write).
EDIT: However, I wouldn't use a continuous form to talk about a past (like "have been VERB-ing" in English), but I'd rather use a normal past tense (madi).