The oldest Germanic word for "wedding" is represented by Old English brydlop (also brydhlop) (liken Old High German bruthlauft, Old Norse bruðhlaup), literally "bride run," the conducting of the woman to her new home. Bride can also mean wedding ... It could also mean the newly wed twosome going to their new home.
In early kennings ("bride-banquet") the brýd could as well mean "wedding" as "the marrying woman", and indeed sometimes ("bridal couple") it cannot to be only about the woman. At first brýd was a broader term which "had the force of ‘bridal, wedding’ (the primitive marriage being essentially the acquisition of a bride)". (OED) Thus the brýdguma (bridegroom) was not 'the bride's man'; he was 'the wedding man'.