If you want a copy of the TWA timetable page for your family file as well, there's one for 1955 on line here :
Index of /ttimages/complete/tw55
Pages 19-20 are the ones for the Frankfurt to New York flights.
All the Frankfurt flights stopped at London as well. The first class flights were notionally nonstop from London to New York, and used L-1049 Super Constellations. The tourist class flights stopped at Shannon and Gander and some (as yours) used the older standard L-749 Constellations which had less range.
N6007C "Star of Ohio", Lockheed builders number 2643, was a typical example of the large Constellation fleet TWA had. Delivered new in August 1950, it stayed on the roster until stored at the TWA maintenence base in Kansas City in February 1966, which was a good long run for an aircraft of that era. It never was sold on, and was disposed for scrap a couple of years later. It was one of a large batch of 20 TWA had built in 1950, registrations N6001C to N6020C inclusive, so you may have better luck tracing a closely comparable aircraft photograph.
A J Jackson's photographs of London Heathrow in the 1950s-60s are a brilliant resource from the period, it seems he took a shot of every aircraft he saw.