In theory, French does not have such present continuous tense, although in past tense, it has imperfect past (imparfait) and perfect past, which contains simple past (passé simple, but not commonly used in modern French) and composite/compound past (passé composé).
However, if one wants to emphasize that at this moment he is doing whatever things, then one may use the construction "être en train de" plus an infinitive (infinitif) afterwards. But then again, it can be substituted by a present tense plus a time adverbial of "en ce moment" (in this moment). For instant,
Je suis en train de lire un livre. = I am reading a book. = Je lis un livre en ce moment.
In conclusion, I would say that you do not need to worry about the structure of present continuous tense. You just take a simple present, plus some certain time adverbial, and it would be fine.