To me is clear they don't end up together.Before their divorce,they were happy in that world of music and parties,and also got married.That meant something stong for both.But,as you know,the things got complicated and they separated and took different ways.Francine and Jimmy were sucessfull in their respective careers and it doesn't seem to me like they really miss each other, but i also think,that,when they met each other again,they felt something,that's why Jimmy wanted to meet Francine for a date.I think they still loved each other,or at least they remembered their old times together and felt like coming back together again.
BUt when they are gonna do it,then,they stop and decided to pursue their lifes apart.So,no,they didn't end up together.I guess they realized their lives had changed much,and really they did not feel like starting a relationship again.
I think they lost the feeling that joined them in the past: music and love.
Each one had a life,both were independent people,and at the end they ended up to not need each other.
There is a deleted scene,where they do meet each other,and walk through the street,talking and laughing.That means they were still friends and possibly their broken relationship and the pain of it,might change to something better.Maybe not a romance, but maybe a positive relationship ,with Jimmy seeing often his son and sharing moments with Francine,to difference of the real ending,where you can see,that, the happiness and the world of showbusiness they shared one day,will not never come back for them as couple together.They had their lives apart.Which is sad,they remain separated forever after everything they shared..
Jimmy Doyle and his orchestra

Scorsese has said that they both had a reconsideration, they both decided not to go through with it. It wasn't one or the other. However on the DVD there is a deleated scene that shows them meeting and walking down the street, so he did shoot a "happy" ending.

No, I don't think so. I also think that Jimmy's heart wasn't really in it, as he loved her enough to realize that it wouldn't be good for her. That self-sacrificing side of Jimmy's personality is often overlooked, in that I feel that in many ways he let her free, as much as he walked out on her and the baby.
"Sometimes you have to take the bull by the tail, and face the truth" - G. Marx

Everything points to the fact that they didn't end together. But the last shot is kinda ambiguous. Like if they were destined to meet each other once again in that chinese restaurant.
Who knows? It's an open ending. It's up to you to guess how it ends and what happened later to Francine and Jimmy.

I have always felt that Jimmy does wait for Francine but it is her decision to blow him off and return to her party. I think Francine will always love Jimmy, but I think she also realized that she had outgrown him and would never take a back seat to him again. Jimmy hadn't changed by the time film endedhe wanted Francine to come back to him and be Mrs. Doyle and she wasn't having that.

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