The two had been together for nine years and had planned to get married. They had lived in London for four months.
The case by Camden Council will be against UK bookmaker William Hill whose sign Marx was hit by.
The trial will be heard at the Blackfriars Crown Court with a 12-person jury and was expected to continue for five weeks.
Hill was criticised in 2015 for "deficiencies" over the installation and checks on the sign.
It came as in inquest ruled the falling shop sign was because of health and safety failings.
Health and Safety Executive inspector Steven Simmons-Jacobs told the inquest that the sign could have fallen down "at any time, with anyone".
The sign was not properly screwed on, and was held up by small "panel pins", which were not designed to hold the weight of a large sign.
William Hill, Saltwell Signs, which put up the sign, and Acean Builders, which carried out a refit, all denied responsibility for checking whether the sign was properly fixed.
The jury at St Pancras Coroner's Court returned a narrative verdict, finding that the reasons for Mr Marx's death were "multi-factorial".
"Despite William Hill having systems in place above the usual standard, there were deficiencies in communication and project management between Acean and William Hill.
The sign had struck Marx's head and neck in front of a number of bystanders.
Five or six people pulled the sign off Marx before ambulance staff, who had been in a passing ambulance, tried to resuscitate him.
He was taken to University College Hospital in Euston but was pronounced dead after suffering a large heart attack as the result of a severe head injury.
