Hi DK,
Yes the 6.5x55 will be fine for the job, but of course so will the .308, better to be over gunned than under as they say, the foxes won't know the difference, and of course it will also take care of the reds as will the 6.5x55 which has a lot of respect in Scandinavian countries, it's been around since the 1890s and still going strong, there are certainly a lot more .308s out there to choose from also a lot more bullet choice, but it doesn't matter what caliber you choose once you find a bullet they like you stick to it.
Here's one to throw you, I have a mate who is in a deer