In American English, the word "family" is usually singular: My family is going to Paris next year. But if you are thinking of the individual members of a family, then you can use a plural verb: My family are planning their vacations: my parents are going to Paris, my sister is going to Berlin, and I am going to Tokyo. (In such a sentence, "family" seems to be mean something like "family members.)

Family is singular, so should be used with is. Plural is families, to be followed with are.