In Final Fantasy XIII-2 (if you haven't played it to the end STOP READING), we know that Snow/Serah is the obvious canon couple. They're engaged, if that isn't obvious enough. They're canon whether we like it or not. While the Serah/Noel dynamic is a bit more ambiguous, we do know that for the most part, they're just friends. Serah never broke up with Snow, and Noel didn't seem to mind their relationship, or even expressed jealousy (it was played with, but it turns out he just didn't like Snow for leaving Serah by herself). Noel also may or may not have romantic feelings for Yeul (but it seems to be leaning more on the latter). When Serah died in the end, Noel cried, shouted her name, stroked her face, hugged her close, and was appropriately anguished. But they weren't romantically involved. Noel just really cared about her, just as Cloud did for Aerith. If Noel did have romantic feelings for Serah, he would be faced with some problems: she's dead, she's getting married (if she lives again; death is cheap if you have time travel), and he also did say he wants to be with Yeul.
I can see how the ending could set a Noel/Serah ship sailing, but if we look at the actual couple (Snow/Serah) and how much they have going for them (kissing and hugging and being officially engaged should be more than enough proof), one death scene which shows an appropriately upset Noel isn't enough to disprove those. In parallel to Clerith and Cloti; Cloti obviously has a lot pointing to them, concretely and abstractly. Clerith has a death scene, Cloti has a family. Aerith is dead and never coming back, and she has Zack mowing the lifestream. Tifa is alive, and she's living with Cloud, with kids who regard them as parents.
That being said, I ship Noel/Serah. But they're not canon.