Unfortunately, thanks to the English reputation for World Cup hooliganism, a swift return to Britain is what he got. When over-zealous French immigration officials found the bat in his luggage yesterday - along with tennis racquets, a football, frisbees and tickets for England's match against Colombia - they labelled him a thug and turned him back.
Mr Eaton, 29, The Independent's head of marketing, was en route to Lens with two friends: Simon Sadie, 29, an advertising media director, and Kal Rahaman, 29, a systems accountant at Channel 5, when he was stopped for routine questioning at Folkestone.
He and his friends, who all had official England Travel Club tickets, intended to board Le Shuttle before travelling to the match and joining two others for a week's holiday in the south of France.
The two other friends, who were not going to the football, had been allowed through by the officials. But once Mr Eaton and his friends said they had tickets for the game, their car was immediately searched.
"We were quite happy to explain what we were up to and that we were bona fide supporters," said Mr Eaton. "The official opened the boot and we showed him all our bags and a duvet and all sorts of rubbish. And then he saw our sporting gear - tennis racquets and balls, frisbees, a football and our softball bat.
"Then he held it up and said: 'Why are you taking this to a football match in France?' And suddenly my heart sank. He thought we were hooligans."
Mr Eaton was questioned at length by several French officials (there is a reciprocal agreement whereby English immigration officials are based on the French side of the Channel Tunnel) and eventually handed a piece of paper to sign.
"They didn't speak much English and I don't speak much French," he said. "But I offered to leave the bat and even leave the tickets, just so I could salvage my holiday, but they wouldn't have it.
"Eventually, they said I had to sign the piece of paper. It was in French but I could make it out as saying we had been refused entry to France on suspicion of causing disorder and we wouldn't be allowed entry for 14 days. One official even had the cheek to ask me how to spell 'baseball bat'."
Mr Sadie watched the drama unfold from the passenger seat. "We had been so excited, but as soon as he picked up the softball bat I just thought 'Oh, God, no. What must that look like?'
"We are the most unlikely football hooligans and we didn't have any football shirts or scarves, but they didn't care. I can understand how it must have looked to them but we were just so helpless. It just shows how the actions of real thugs are affecting all our reputations abroad."
Laurent Lemarchand, the deputy press consular at the French embassy in London, was not unsympathetic to the fans' plight - but he added that he considered their actions a little silly. "This is probably the worst day of the year to try to take a baseball bat into France," he said. "The immigration police evaluate the evidence available to them and make their own decision. There is nothing we can do to change it." He said that the men had been given the reasons in writing and had signed them.
Mr Eaton and his friends point out that those reasons were in French and they had been told they could not leave until they had signed. "Their behaviour is ridiculous," said Mr Sadie. " It is a another example of the French not playing ball with the English."Reuse content