C.P.
Talk to his teacher directly. While SOME of that is pretty normal boy behavior, the teacher has a pretty good idea (since they've dealt with numerous 6 year old boys) of whether his inattention is abnormal or excessive.
For inattentive and hyperactive boys (like mine, who are now 8 and 10), I STRONGLY suggest some physical activity in the morning before school. My boys walk to school and then are able to run around the playground for a while until breakfast. This helps them to get some of that wiggle out and allows for socialization and a little fun. I've noticed that they tend to be less trouble and have better behavior in class when they do this.
It's hard on a kid to tell them "you have to go straight from home to sitting in class for several hours before you can get some wiggle time in." And I think it's simply ridiculous to tell a hyperactive kid not to fidget if you don't let them get some energy out!
Good luck!