In short, yes, in a parliamentary democracy, such popular protests have a significant influence on policy.
Then how come Canada and Britain don't have protests like the French?
The Canadian and British government structures are different from the French, and are essentially two party systems like ours. The French, like most continental countries are multi-party systems with direct, proportional elections. The English and Canadian systems are more like ours, and are de-facto two party systems. This allows voters a sense of access to their representatives, real or imagined, that is missing in a proportional, national, voting scheme.
