Beav,
Those class ratings are pretty consistant in terms of difficulty from one river to the next, even tho the rapids have different character.  Compare the rapids you have been on that have class II+ ratings and decide if you would be comfortable running them with your girlfriend.  You can always portage after seeing the rapid.  I can tell you that class III is solid whitewater and in a kayak I am dumped 50% of the time.  Class II is a mandatory scout of the rapid with an open canoe.  I have found rapids to be rated class II because of standing waves or "haystacks" which follow a drop of up to 4 feet.  If you don't have a boulder garden below the drop, you should be fine.  Plan on getting water in the canoe.  Rapids are also considered class II when they are long and continuous. Maneuvering and bracing skills are required at least in the stern. You should have no problem here.  Class II+ is getting marginal for an open canoe without WW experience. June water temps on the Bois Brule should be in the low to mid 60's. I would recommend not taking your tripping canoe.  Iron River, Wis. has at least one big livery that will rent you a durable river canoe.  Have fun.
-YB