So if it was "Am Morgen" than it would have been translated to "Morning"? How can I tell when it is Morning and when it is Tomorrow?
Am Morgen or morgens translate to something like at the morning. Then you have either the am or the s. When you see neither then its Morgen/tomorrow (or you could see it with an article, then its a morning / the morning).
As written, 'Morgen' can only mean tomorrow, not morning. If you wish to begin the sentence with 'tomorrow morning' the sentence would then read "Morgen früh ........... I also find it awkward to use the verb 'gehen' in this sentence, with a named destination such as Paris, as that verb generally implies 'to go by foot.' It would be more common to use 'fahren (mit)' or 'reisen (nach),' instead.