I, like you, somehow thought that he was entering his third year. Maybe because his confidence level seemed more third-year-ish, and Lily was two years behind Albus, so I thought Albus would be two years behind James.

Then I think I read in one of fernwithy's Teddy stories that the boys were only one year apart and I went back and read the epilogue. The reference Ginny makes to the letters she wrote James the previous year seem to imply that he was only a year ahead of Albus, but I think you could interpret it either way, it depends on the tone which Ginny delivers the line and the subtext:

"We wrote James three times a week last year." (if she emphasized the last as I did, then the subtext could be: "and that was his second year."

JKR didn't put the word in italics, but that doesn't mean Ginny didn't speak it just that way.