The Economist has a collection of videos here, in one of which several worthies speculate on what would happen if, to ensure a win in the coming French presidential election, and a defeat for Marine Le Pen, the candidates had to offer to hold a referendum on France’s continuing membership of the EU. One participant suggests that the French dislike the EU even more than the British do, and so would vote to leave.
How would the EU mandarins respond? Two possibilities are worth considering. They can be labelled the ideological and the pragmatic responses. In the ideological case, those who must be obeyed take the view that their Project is so important and precious – and dependant on the participation of France – that they cannot allow France to leave. The pragmatic response would be to acknowledge that the Project has failed to convince sufficient citizens that they can expect to benefit from it and so must be terminated as smoothly as possible. 
The Brexit vote has caused a rumpus because it is the first time a member state has proposed to leave. But Britain has always been a half-hearted, discontented member, while France was a founder member and critical to the EU’s development and future. Britain’s departure will be an inconvenience; France’s would be terminal, if allowed to happen.
The choice the mandarins make would be highly significant for the world at large. Either way, for an unknown period Europe would be in disarray. Trade relations and much else would be even more uncertain and volatile. If the mandarins clung to their imposed ideology then the disarray might become violent and possibly spread beyond Europe’s borders. 
In the unlikely event that the mandarins chose the pragmatic response, politicians and civil servants across the EU would have to work night and day to unravel the complexities that have been created over more than 60 years. A bit like trying to clear your garden of bindweed.
How might the rest of the world react? America, and possibly China, would probably press the EU to be pragmatic. Russia under Putin would surely see a riotous breakup as in its interest and so try to provoke an ideological response. Reactions from elsewhere, with the possible exception of the UN, would be less significant.
The Eurasia Group, a research and consulting company, assessed the likelihood of Brexit contagion and published the result in this chart:
Ian Bremmer, President of the Eurasia Group, said, “Nearly every European state is now grappling with stronger fringe party candidates at home, with large populations (generally from 30%-60%) in favour of getting their own referenda…. To be clear, it remains quite unlikely any of these fringe party leaders can actually win in Europe’s major countries, but the process of buying them off will be challenging, and far more so if exiting an increasingly broken EU looks like an ever more plausible option from the perspective of the domestic populations.”
This EU Won't Work 