Or Picard could have been a very adept learner of English. His Anglophilia may have been part of his brother's annoyance with him.
His brother who also had an English accent? And whose wife and son had English accents too?
It's worth keeping in mind that they have transporters in the 24th century. Schoolchildren in La Barre could commute to London for school as easily as they could commute to the nearest town.