The most important thing to realise is that the English present perfect (have done) might correspond to the French passé composé in form, but it does NOT correspond in to it in use. We use the present perfect in most cases to refer to unfinished periods of time and the past simple to refer to finished periods of time. The present perfect always has a link with the present and tells us something about the present situation. 'Je n'ai pas vu Pierre ce matin' can be translated in two ways. If it is still morning now, you would say 'I haven't seen Pierre this morning'. This is connected with present time, in that you are perhaps still expecting to see Pierre, and it is still possible that you will see him during the course of the morning. If it is now afternoon or evening, you would translate this sentence as 'I didn't see Pierre this morning'. This refers to a finished period of time.