A little bit later, but would loosely match the season 2 episode Playtime of Seaquest DSV, first shown in 1994.
The Seaquest travels 225 years in to the future, where humanity has mostly given up meeting in person in favour of interacting (mostly battling) in VR. The last two people alive - conveniently one male, one female, and both teenagers - are persuaded to start interacting in person again.
I last watched the show probably 15 years ago so detailed memories are a bit hazy. Having found a set of badly dubbed clips, the penultimate scene does appear to show them walking off hand-in-hand.