I didn’t read what The Fortune Men was about ahead of time, because I was reading it for my Booker prize project. That meant that at first I wasn’t sure why the novel switched between the stories of two characters, Mahmood Mattan, a Somali stoker who is a gambler and a petty thief, and Violet Volacki, a middle-aged Jewish storekeeper. However, when I turned to the back of the book, I learned that Mattan was the last man in Cardiff to be sentenced to death for the murder of Violet Volacki in 1952 and that years later he was found to have been wrongfully convicted.
Mahmood is not a perfect man. He has quit going to sea to be near his Welsh wife and children, but work is hard to find for a black man, and he has too much time on his hands. He spends it gambling and womanizing and occasionally stealing. He has a big mouth and he lies a lot. But he is not a murderer.
When the police come to see him because a woman was robbed and her throat cut, he doesn’t tell the exact truth about where he was, because he was dangling after a Russian woman and he doesn’t want his wife to know. A black man, possibly a Somali, was seen outside the store, but even after the victim’s sister and niece say it was not Mahmood, it’s pretty clear that the police decide it was him and look for people to place him there. After a reward is announced, plenty of them pop up.
This novel is well-written and should have been haunting, but first I kept having problems staying with it, and later, even after I got more interested, I felt distanced from the characters and the story. Mohamed went on side trips through the memory of Mahmood’s life that should have made readers feel closer to him, but I did not, and I noticed Goodreads reviewers complaining about the same thing.
whatmeread 
I liked the sound of this one when it came out, but the reviews put me off a bit, for much the reasons you give. Pity, it’s a good premise.
I don’t know if I would not read it if it sounded interesting, though.
I thought this was an interesting book, particularly as it was based on a true story, but I didn’t love it either. I agree that the parts about Mahmood’s backstory didn’t work very well.
I guess there wasn’t enough story there to make a complete book without the backstory.