But, believe it or not, the two of them had an incredible interaction when they met at Buckingham Palace in 2007.
So, as many Brits thank the Queen Liz's Platinum Jubilee for giving them an extra two days off, talkSPORT relives the time the former Arsenal defender asked if he could retire as a footballer so he could dog sit the royal corgis.
Yes, that actually happened.
Eboue told The Telegraph in 2016: "We went there and Thierry Henry said to me: 'Please, Emmanuel, this is Buckingham Palace, it's the Queen's house, don't do anything.'
"'No problem,' I said. 'Don't worry.' So the Queen came in and went along shaking each player's hand.
"After she'd finished I saw all her corgis so I said, 'Ma'am, Ma'am'.
"She turned back and asked, 'How are you?' and I said, 'Ma'am, I am OK thank you but, please, I don't want to be a footballer anymore.'
"'I want to look after your dogs. I want to take them for walks, wash them, feed them. I want to be a dog carer.'
"The Queen, honestly, she was laughing. Prince Philip was laughing, too. All the team were laughing."
It's still unclear as to whether Eboue was joking, but there have been plenty of his ex-teammates who recall him being the dressing room jester during his time at the Gunners.
Unfortunately, his apparent obsession with the Queen and her beloved corgis never led to a job within the monarchy for the Ivorian.
Instead, he went on to make 214 appearances for the north Londoners, before moving to Turkish side Galatasaray.
But, rather than finishing his playing career at Sunderland, a move to Queens Park Rangers, Crystal Palace, or the Royals of Reading might have been more apt.