It is 'pidgin English,' not 'pigeon English.' A pigeon is a type of bird :) Linguistically speaking, a 'pidgin language' is a simplified form of a language to allow people who do not share a common language to communicate with each other. However 'pidgin' can also be used as an insulting term for someone who doesn't speak a language very well. If someone says another person speaks 'pidgin English' it means that they don't speak good English. It would be odd for someone to describe themselves as speaking 'pidgin English,' it's not a complementary term.

It should be "pidgin English". So that means a mishmash of broken English plus interference from the speaker's first language.