I heard a lot Chinese people and French/Italian people are linked, e.g. they both love to eat and drink, and family is very important for all of them. But what about the relationship between the future ex-1rst superpower, aka the United States of America and the future 1rst superpower aka China ?

This is the topic of a new book: “Partners and Rivals: The Uneasy Future of China's Relationship with the United States”, written by an economist, Wendy Dobson. This University of Toronto professor emphasizes the asymmetry in the familiarity with US strengths and weaknesses, and lack of familiarity with China's huge domestic challenges and view of the world.  
In her book, she examines how each views itself and the other, how China views the world and the existing institutions, and how and why they can and should cooperate. You could find some insights in this video: http://youtu.be/nkog-PhnR4k. Speaking of it, using Youtube as a video channel to broacast a news in China and in the US is already a proof of misunderstanding the Chinese usages.  
If the USA/China rivalry topic is intersting you, there are already many books on this subject: 
- On China by Henry Kissinger 
- What the U.S. Can Learn from China: An Open-Minded Guide to Treating Our Greatest Competitor as Our Greatest Teacher... (Ann Lee and Ian Bremmer)
- The China Choice: Why We Should Share Power (Hugh White)
- The Endless Crisis: How Monopoly-Finance Capital Produces Stagnation and Upheaval from the USA to China (John Bellamy Foster and Robert W. W. McChesney)
By Renaud Edouard-Baraud
CEO of L'Atelier BNP Paribas Asia