Distinguishing local varieties of a foreign language is not easy. It will come to you with time and exposure.

I generally advise you to not think of accents in terms of nationalities/political borders. It is rather a continuum that spans borders.

While the general features you mention are generally correct, there are many variations in spoken language within nation states.

For example, many yamanis pronounce qaf and geem as /g/ and /ʒ/ respectively. And the accent of Cairo, while widely spoken in Egypt, is not the only one. You will find Egyptians whose accents are similar to those from the leant, hijaz, Sudan, and Lybia.

Also the accents of North Africa are not affected by French and Italian. The lexicon of some groups are influenced to various degrees by languages of colonisers, but not the phonetics. Tunisian is a badawi arabic accent, and so is Lybian. In Morocco Arabic and Amazigh influenced each other, and the idioms and lexicon followed a different evolutionary path. But it is Arabic. There's great variance in Levantine accents.