The Benin international, who was a Sunderland player at the time of the offence in August, also pleaded guilty to two counts of driving without a licence and driving without insurance.
The charge of having no licence related to an earlier incident in February.
Appearing at Newcastle Magistrates' Court, Sessegnon was given three points on his licence and was ordered to pay £7,605.
The 29-year-old was more than double the drink-driving limit when he was stopped by police in Newcastle ahead of Sunderland's 4-2 win over League One side MK Dons in the Capital One Cup.
Mrs Judith Williams, prosecuting, said: "At 6.35pm on August 27 officers were drawn to reports of a Range Rover driving down Westgate Road, Newcastle.
"Further checks found that the vehicle was not insured. Officers spoke to the driver and checks found he was unlicenced.
"He also failed a road side breath test."
Mr John Kirkham, defending, explained that Sessegnon had "fallen foul of a peculiar quirk" as his licence had enabled him to drive in France which he mistakenly believed would allow him to drive in other EU countries.
As for the drink-driving offence, Mr Kirkham said: "He's very apologetic, he had consumed some wine and then slept.
"He was going to collect his sister from Newcastle City Centre."
Sessegnon does have the opportunity to reduce his ban by five months though, if he completes a drink driving rehabilitation course.