This will focus more on 20th century history but hopefully someone else will add a comment.

Quebec and Louisiana both have passed measures regarding the French language, however the differences between Louisiana's legislature from 1968 and Quebec's Charter of the French Language (1977) mean that francophone culture in both areas has been kept alive in very different ways and for different purposes, with Quebec's Charter arguably being more effective at allowing the French language to enjoy special status in the province.

The ratio of native English speakers to French speakers in the USA versus Canada are quite different. In Canada (as a whole), native French speakers make up just over 22% of the entire population, whereas in the United States only about 0.44% of the population speaks French. In more precise numbers: In Canada, 7,298,185 people (according to the 2011 census) have spoken French since birth, whereas in the United States only 1,307,742 people speak French, fluently or otherwise (according to the 2013 American Community Survey). Therefore, French speakers in Canada have far more leverage when it comes to keeping their culture and language alive, especially through government policy.

French was first declared the sole official language of Quebec in 1974 through the "Loi sur la langue officielle" ("Official Language Act"), meaning that French was made the official language of instruction in schools (limiting the use of English to native speakers), the language of all services, the language of all government AND commercial signage, the language of business in Quebec (businesses have to go through a "francization" process), and that French was given priority in cases of ambiguity of the law. Further, in 1977 the Charter of the French Language was passed which remains to this day. The Charter follows generally what was outlined in the prior Official Language Act, and also established councils to ensure that Quebec's language laws were being followed.

French speakers in Louisiana, unlike the Quebecois, have historically faced a much more rigorous attempt at stripping them of their French language -- in 1915, English became the language of education, meaning that native French speakers were forced to speak English in school. French was stamped out through force.

Thus began the decline of the francophone population, which (as of the 2000 census) only amounts for 4.7% of the population versus the 90.8% English-speaking majority. In Louisiana, French does enjoy special legal status, however the purpose of this legislation is arguably more focused on promoting tourism and heritage than Quebec's legislation (which is focused on French as a very much alive majority language). State employees are not required to speak French but are encouraged, French immersion programs are promoted, and most importantly French heritage and tourism is promoted. This legislation is much less vigorous and all-encompassing than Quebec's as the francophone community in Louisiana has been on the decline since the early 20th century, whereas in Quebec they have thrived due to being the majority and not being subjected to the same assimilation efforts.

TL;DR: French in Louisiana was forcibly stripped from its speakers in the early 20th century, whereas in Quebec French speakers have always been the majority and didn't face this degree of assimilation. 20th century legislation in both areas attempts to keep French alive to varying degrees of success and for different purposes (Quebec: because everyone speaks it, Louisiana: tourism $$)