Delaroche's painting is dated to 1831, he had a 'straightforward technique that was firm, solid and smooth' he also had a wonderful talent for the dramatic. He was known to build little stage sets, including model figures to aid his work, he was also well known for his cloaked references to the French Revolution in which he often used English historical 'victims' such as Charles I, Lady Jane Grey and Thomas Wentworth to make a point.
So what does Delaroche mean when he depicts Cromwell holding open the coffin with one hand while he rests his other against the hilt of his sword. Maybe Cromwell's reflecting on his success as he stares at Charles's face and his sword is a physical reminder of how he and the English parliament brought down a king. What a perfect way of representing the revolution in France. With the troubles too recent to depict directly, Deloroche uses the regime change in England and the execution of Charles to explore the change of fortunes and the fall of the French monarchy.
It is a probably a myth that Cromwell raised the lid of Charles's coffin and stared at the kings decapitated body, but this fact did not deter him, Delaroche cared little about historical inaccuracies if he succeeded in getting his point across to the French public.
Another good example of this is his painting The Princes in the Tower, for which he drew his inspiration from the work of Shakespeare, a story he knew to have some truth. With this in mind he was able to make a comparison of the deaths of the two English boys to draw attention to the mysterious deaths of Louis XVII of France.