French is spoken in Quebec (and other areas of Canada) because the first Europeans to settle in the area were French. As the generations continued, French was the language that was passed down,. Today, many people who live in the province have roots that can be traced back to these European settlers. 
Over the years, there have been many conflicts in the province that have threatened the French way of life. The most well-know of such conflicts was in the 1760s. France and England fought over control of both the province and Canada, as a whole. Since then, the mixture of British and French culture and laws have been apparent.