I have a 12 gauge franchi I-12, and it doesn't appear to be aligned exactly right.

I have switched the shims, with no success.

I have heard about a process where a gunsmith can correct this by putting a slight bend in the barrel to make it straighter or to correct the prblem.

Has anyone done this before? What was your cost? Is it better to just get a new barrel?

whenever I go to shoot clays, I outperform the franchi with my remington 870 em 20 gauge.

Yes a good shotgun smith can do exactly that. I've got two friends that had it done. In one case, the smith bent the magazine tube, which realigned the barrel. The cost was minimal, on the order of $25.