A good question.
Two quick comments. First, do you notice that (in Gal 5:22-26) it is not the ‘fruits of..’ (plural) but the ‘fruit of..’ (singular)?
Although we can look at each of the characteristics individually it is worth noting that this list including love, joy, peace, patience, kindness, goodness, faithfulness, gentleness and self control is not an exhaustive list (what about hope? – c.f. 1 Cor 13:13) and so they collectively indicate many of the marks of the Christian person – the person who lives by the Spirit.
Second, they are characteristics of a person which indicate a way of life. Note that Galatians 5:23 comments (at least concerning the fruit) that they are not regulated by law. Personal characteristics and qualities cannot be regulated by law and so in this sense we can say that the fruit of the Spirit does display personal characteristics – at least desirable ones! Further, the ‘fruit of the Spirit’ list is in contrast with the ‘acts of the sinful nature’ (Gal 5:19-21). Both lists indicate a way of life which is internally driven and externally obvious in the person. So yes, in my mind, personal characteristics.