Shep at the end

I never took it as him being particularly sad about the baby, but about her. I think Shep was totally infatuated with her.

The one night they slept together in the car she was already pregnant, and he knew that...
Remember she was talking to him and crying on his shoulder because she was depressed about not being able to go to Paris because of it

After they have sex he says about having wanted it for the longest time and admits he's been in love with her... pretty much confirming that they'd never slept together before that

So no, he wouldn't have thought it was his... I think he was just obsessed/infatuated with her

Funny you asked this because I just watched the movie for the 3rd time and I was going to post the exact same question with the exact same subject line. Of course the other posters are right about her already being pregnant, but on this viewing I had the same question at the end.

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Shep already knew that April was pregnant, before they had that "quickie" in the car.
But..... Shep did tell April that he "loved her" (in that car), plus the way he looked at April during that scene where she is by the door with a sexy look on her face early in the movie, you can tell that Shep had a "thing" for her.
So he probably cried because he had "lust" for her along with some "caring" for her.
So that's why Shep cried.
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Shep is April. Unhappy. Discontent. Playing house. He found momentary happiness with her not understanding that she only used him because she hated her life. He hates his life.
Shep's scene at the end is showing that he is no different.