As with so many grammar questions, the answer is 'it depends'. If usage is split, there's invariably a reason for it. In this case, the issue is one of 'notional concord' - that is, the verb agrees with the part of the subject that is most important in the speaker's mind. If the sentence had been The jeans are on the table there would have been no problem. The subject consists of just one notion, so there is no choice to be made, and normal 'grammatical concord' operates, with the plural verb.
As soon as you say 'A pair of jeans' two notions are brought together and now there is a possible choice. If 'pair' is the notion the speaker is focusing on, the verb would be singular according to normal grammatical rules. But the question arises: why would anyone ever want to do that? Pair is simply a routine summation noun. There is no semantic contrast. One wouldn't normally try to say 'I have a pair of trousers, not a --- of trousers'.
But as soon as pair is modified, things change. The first pair of jeans allows a contrast with later pairs. Now speakers have a semantic choice to make. If the notion of 'first pair' is dominant in their minds, they will go for singular concord. If, notwithstanding the adjective, they are still thinking of the sentence as being about jeans, they will go for the second. But surely the reason for saying first pair is to make that notion semantically pre-eminent - otherwise why say it at all? In which case I'd expect to see singular concord following.
And what happens (I hear someone saying) if both notions are equally important in the mind? Well, semantic reasoning is now ruled out, and people have to resort to other factors. If you have been steeped in a prescriptive grammatical tradition, you will follow the traditional recommendation, and use the singular (as in a number of and other such phrases). In everyday speech, however, 'concord of proximity' is the main influence - that is, we make the verb agree with the nearest noun - so the concord will be plural. When a 'grammatical' user and a 'proximity' user meet each other - as sometimes happens in the usage column in a newspaper - then sparks can fly!