I think Harris's publishers knew that many gammons, as they are now called, like alternate history stories, especially ones around the Second World War and such a cover would appeal to them. The achievement for Harris was that this was probably the first AH book since SS-GB (1978) to crossover into mainstream sales at least in the UK. It is a shame that the movie did not get wider showing. I have been told it was because too many in US audiences, especially in the 18-30 group, did not comprehend that the Germany in 1964 being shown was an alternative and somehow believed it was a portrayal of East Germany. Coming out in 1994 it also fell into that awkward period of being on video when they were on their way out. For some years I know someone sold DVDs copied from the video, but not of high quality. In addition, I have not noticed it being shown on television, but given the number of channels now, I may have missed it.
With spoilers:
One problem I have with Harris's books, and Enigma (1995) is another example, is that he really struggles with endings. The closing scenes of Fatherland with Xavier March driving across a chunk of Germany into the old Poland, being pursued by the authorities not pulling him over, seemed very weak. The movie's denouement of Charlotte Maguire getting into President Joseph Kennedy's car and presenting him with details of the Holocaust, while still dramatic, seems just that little more reasonable. It is not often that screenwriters improve on the source novel, but I certainly feel this is one case.