I'm playing a Breton. I've never done the Civil War yet, because I never know which side to go with. I don't feel strongly either way. But, this time I want to do it. And, I want to know what my character may feel as a Breton. Do they have any stakes on either side?

High Rock itself is part of the Empire.

The Reachmen/Forsworn are Bretons. so the way they've been treated in the past may be a valid consideration.

You can ignore all the hype regarding both sides and consider other factors, if you choose.

First time I played the CW was as a Breton. I joined the Imperials largely because my house was in Whiterun, and I was defending it ,

Bretons have no inherent interest in the Skyrim civil war as far as I know. The political situation in High Rock is currently unknown so we do not know what their opinion on the current Empire is, but since High Rock is still a province still and there is a Breton Legate, I'd say they are more likely to be pro-Empire. Of course, that is based on what little evidence we have and is not conclusive at all.