In this scenario, James could at least be detained on reasonable suspicion for involvement in murder and perhaps arrested if there is probable cause to think that he was involved based on previous incidents that the police already know about and on further evidence. Let's look at this in more detail.
During the fight a week before the murder, James physically assaulted Janice, which shows that he has the capacity for violence. He also offered a verbal threat against Janice's life. Janice had the presence of mind to call the police, and even though James left before Officer Smith arrived, the incident was officially recorded and a complaint made. This establishes the violence already committed and would certainly make James a suspect in the murder.
Janice, however, chose not to pursue a restraining order. If she had done so, she may have had another means of protection against James, although he certainly might have violated the order. At least the restraining order would have provided further evidence about the nature of the relationship.
When Janice is found murdered, then, the police would naturally turn to James as a suspect, considering the past complaint. They could detain him on reasonable suspicion, a common-sense conclusion about how people often behave. James has been violent in the past and may have been again, especially with the death threat. But reasonable suspicion is not enough for an arrest. That requires probable cause based on evidence.
Let's say, for instance, that as the police are investigating the crime scene, they find fingerprints that match James's, or they find other forensic evidence that points to him or a print that matches his shoes. A neighbor might have seen what looked like James's car at Janice's home on the night of the murder. Evidence like this would be enough to arrest James for murder on probable cause. It would not yet prove a murder charge against him, though, so officers would have to find more evidence and continue to build their case.