In 1901, there is a Francis Innes at 39 Red Rock St, West Derby (RG13/3498 ED 6 Fol 111 P 4).
Francis Innes, Head, M, 36, Plaster, own account, Edinburgh
Elizth Innes, Wife, M, 35, Liverpool Lancs
Eliz Frances Innes, Daur, 11, Liverpool Lancs
Mildres Innes, Daur, 8, Liverpool Lancs
In the light of the place of birth, William might be north of the border with other relatives. If so we will have to wait for the census release on Scotland's People.