There are a range of possibilities, depending on the exact relationship. If the niece is the daughter of one of his cousins (i.e., they are the child of one of the cousin's brothers or sisters) they would be a second cousin. If they are the child of one of the cousins' brother's or sister's spouse, there is no relationship, though most families would probably refer to them as a distant cousin.
They are of no blood relation. But they are cousins by marriage or 'step-cousins' as such.
cousins
Your son and your niece are first cousins.
Your child and your niece are first cousins to each other. Your child and your niece's child are first cousins, once removed.
Your great great niece is the granddaughter of your niece or nephew. Your daughter and your niece or nephew are first cousins. Your daughter and your great great niece are first cousins, twice removed.
You would be second cousins.
Your granddaughter and grand niece are second cousins to each other.
Your daughter and your niece are first cousins. Your daughter than your niece's son are first cousin's once removed. Your daughter's child and your niece's child are second cousins to each other.
Your granddaughter and your grandniece are second cousins or third cousins to each other
Your children and your husband's niece are first cousins. There is a difference of one generation between them. That makes them first cousins once removed.
Your niece and your son or daughter are first cousins. That would make your niece and your grandchild first cousins once removed. Your niece's child and your grandchild are second cousins.
Your fathers brothers are your uncles. You are their nephew, or niece.