。
She speaks English with a foreign accent.
Literal
She [topic-は] foreign-accent [subject-の] exist English [object-を] speaks.
外国なまりのある英語 is a noun-modifying clause built around the existential ある: literally 'English (in which) a foreign accent exists,' i.e. 'English with a foreign accent.' Notice the の where you might expect が — inside a noun-modifying clause, the subject marker が can be replaced with の, and short ある/いる-clauses like this one are the most natural place to see that swap. The word なまり covers any non-standard accent, foreign or domestic — 関西なまり, 東北なまり, and 外国なまり are all formed the same way.