The couple were spotted walking along the road between the White Horse Pub and Le Marais around 23:30 on Saturday 30 June.
As they continued along the road heading east, Police said the man punched the woman “several times.”
The incident is being treated as a “domestic assault” by Police, who described the alleged perpetrator as white and 5”10 with short dark hair.
Pictured: The man and woman were reported as walking from the White Horse Pub in the direction of Le Marais.
The woman with him was said to be “tall and slim with shoulder-length brown curly hair, and possibly wearing a peach-coloured t-shirt.”
Anyone who may have witnessed the assaults or who was in the area at the time is urged to call Police on 612612. Anonymous reports can be made by calling Crimestoppers on 0800 555111.