Part of a decorative stone column broke away from the front wall of the building above the restaurant in Battersea Rise at 9.20pm on Wednesday, killing 27-year-old Peter Westropp instantly.
Witnesses claimed it crashed through the awning on to him as he sat drinking with friends at the award-winning restaurant.
The Metropolitan Police said that he was pronounced dead at the scene and the cause of the incident is being investigated on behalf of the coroner.
Wandsworth council has urged shops, restaurants and other businesses to make regular safety checks on their buildings.
A statement from the council read: “The area where the incident occurred was not affected in any way by the disturbances in Clapham Junction town centre earlier this week.”
Strategic planning spokesman Councillor Russell King said: "This was a tragic incident that underlines the importance of all property owners making sure that their buildings are properly maintained and do not pose a risk to the public.
"Businesses in particular need to make sure that their landlord carries out regular checks on the condition of their properties so that they can see if any defects have developed.
"This is particularly important for businesses like pubs, bars and restaurants which have customers sitting or standing outside their buildings for prolonged periods of time.
"Commercial property owners need to employ structural engineers or surveyors to periodically inspect their buildings. This should not cost a great deal of money and it will enable these owners to quickly spot any problems and immediately remedy them."
Director of Le Bouchon Bordelais, Frederic Ollier said: "All of us are deeply saddened.
"An investigation has begun but it is apparent that these injuries resulted from masonry from premises above our restaurant.
"Whilst these premises do not form part of the restaurant, we are anxious to co-operate with all inquiries. We offer our condolences to the family."