"It has been a long convention in English phonetics and phonology for the phoneme /r/ to be represented by the symbol “r”."
Narrow Phonetic Transcription - Azus Notes
I have learnt that phonetics studies all sounds of languages. So, there is no English phonetics or French Phonetics but English phonology, etc.
Correct me please.
No. I think by your second-last sentence you mean '...the symbols agreed by the International Phonetic Association are designed to represent the sounds of all languages'. But those few symbols, with added diacritics, can represent a few thousand 'ideal' sounds. The human buccal tract is capable of producing an unlimited number.
Look up 'allophones'. English speakers represent the phonemes of English by producing various allophones. That process can be called 'English phonetics'.
I'm not sure what the first sentence means, but there is nothing wrong with the phrase 'English phonetics and phonology'.