It is Arthur Sadoun, who replaced Lévy as chairman and chief executive of Publicis Groupe in June, passing through the restaurant with a senior executive from Dutch brewing giant Heineken. The trio warmly exchange pleasantries ahead of their audience with the International Monetary Fund managing director Christine Lagarde later in the day.
In an analyst call ahead of him stepping aside after 30 years in charge Lévy joked that he was "not even semi-retiring" and would be there to do whatever the management needed, even "shining their shoes". It seems Publicis Groupe’s executive has wisely decided the new chair of its supervisory board is more useful organising events with global political leaders than running errands.
But even if there is no sign of him slowing down, Lévy is in a reflective mood. When he took over of Publicis Groupe it was a "family-owned and family-controlled business in an environment which was against capitalism and against advertising." In fact, advertising and marketing was so unpopular in France Lévy describes the common attitude as "publiphobia".
"When I started in that business I was looked down by all the people I knew because I had chosen to work in an industry that was not considered as one of the noble industries," Lévy continues. "In my family they didn’t understand [why] I have chosen to do that rather than to be a doctor or a lawyer."
How things have changed. Just as Lévy’s first job as an agency head of IT grew into him becoming chief executive, that "family-controlled business" is now the third biggest advertising holding company in the world with a market cap €12.7. "We won huge accounts, huge credibility," Lévy says proudly. "We have innovated more than any other agency."
One of the things he’s most proud of is Publicis Groupe’s bombastic $3.7bn purchase of Sapient. He says it is helping the group transform its clients’ businesses, not just their marketing. Another notable recent change was the restructure into four solution hubs (Publicis Communications, Publicis Media, Publicis.Sapient and Publicis Health) to enable the group’s specialists to organise themselves around clients’ needs, something it has called the "Power of One".
"People were laughing at the beginning and some of our competitors were looking at us and saying ‘oh it’s a small thing’," Lévy says. "Now they are all considering that the idea of the Power of One is a great disruption in the industry. That being one company and eliminating the holding company level is something that is sensible to best serve our clients."
Anecdotally it seems to be paying off. In the initial period after the aborted merger with Omnicom it appeared Publicis Groupe was struggling. The group’s pre-tax income fell by 5.5% in 2014 compared with 2013 after what Lévy described as a "patchy year". Since then the restructure into solution hubs appears to have – anecdotally at least – encouraged cross-agency collaboration. In the second quarter of this year Publicis Groupe reported the second highest organic growth of the big six holding companies, behind Omnicom.
"When I look back, which I never do," Lévy says, before somewhat contradicting himself. "So, when I look back, I think Publicis is the best position to do to best serve our clients. Big on data. Big on transformation. Big on classic communications services and more importantly on media and creative. Even if we went through a bumpy road I’m extremely proud of what has been achieved.
"Because the changes we did are deep and today most of our competitors are looking at ways to imitate what we have done. We are two years ahead of them, which is a very good situation."
Lévy says he is "personally extremely sad" about the UK leaving the European Union, although Publicis Groupe’s UK business is currently benefiting from the devaluation of the pound. He is critical of last year’s Remain campaign – describing it as "terrible" – and contrasts it with Emmanuel Macron’s successful campaign for the French presidency, which showed a "positive and constructive message can win".
A softer Brexit may be better for the UK economy, Lévy says, although he concedes he "still doesn’t know what that means" and acknowledges the free movement of people was at the core of the reason many British people voted to leave. "I am happy to not be a politician in the UK," he quips.
If he’s not looking for a second career in UK politics, Lévy is looking forward to giving more time to his work for good causes. He co-founded the French institute for Brain and Spinal Cord disorders (the Institut du Cerveau et de la Moelle Épinière or ICM) in 2005 and is the chairman of the board of governors for the Peres Center for Peace in Israel – a cause "extremely dear" to his heart. He is also president of the French committee of the Weizmann Institute of Science.
Sadoun’s joke about Lévy being really in charge suggests the duo is comfortable with the new order of things. And Sadoun has certainly had a busy first four months as the boss, pulling out of all awards schemes and continuing Publicis Groupe’s global restructure with a new data and analytics division, Spine. Lévy says they are working "extremely well" together but declines to put a time frame on his new role: "My goal is to help him and to support him. So as long as I will be useful I will stay."
So, whether Sadoun’s loafers are looking a little scuffed or he needs a star speaker for a client event, Lévy will there for him to turn to. When he’s not busy brokering peace between the Israelis and Palestinians, that is.