Based on the information given, the match could be on either the paternal or maternal side.
A woman has two X-chromosomes, and she inherits an X-chromosome each from her mother and father. Of course her autosomal DNA is 50% from her mother and 50% from her father.
Without further information and analysis, such as matching those segments with other cousins, there is no way of knowing whether the match is from the mother or father. If you have other matches on that same X-chromosome, and you know which side of the family they were on, then this match must also be on that side. For example, if you have another match on the same X-chromosome for a first cousin on your mother's side, then you know that any matches on this X-chromosome must also be from your mother's side.