The couple were caught on CCTV standing on a line near Whitby in July.
More than 5,000 trespassing incidents were recorded between June and September, with many involving people using the railways as a backdrop for photos.
Network Rail said taking selfies and photo shoots was “plain stupidity”.
In September alone some 1,239 incidents were recorded – a 17% rise.
Supt Alison Evans, of British Transport Police, said: “The railway is not an appropriate or safe setting for a photographic backdrop, no matter how scenic the setting.
“Every time someone strays on to the rail network they are not only putting themselves at risk of serious, life-threatening injury, but also delaying essential journeys.”
Network Rail has launched a “You vs Train” campaign in partnership with British Transport Police to highlight the issue of young people trespassing.
The number of incidents involving children at 51 targeted locations has fallen in each of the past two years.
Allan Spence, of Network Rail, said: “Wedding photos or selfies on the track are just plain stupidity.
“Please, make sure you know the rail safety basics and pass that knowledge onto your loved ones. Lead by example and stay off the tracks.”