The "multilingual turn" brings questions of language ownership to the forefront of debates about linguistic minority governance. Acadian minority cultural producers construct language ownership using multiple languages and targeting multilingual publics, but use ideologies of monolingualism to situate Acadian authenticity in place and time. As globalization brings minority language governmentality onto global terrains, cultural workers manage the tension between multilingualism and ownership through affective registers. This paper contributes to theorizing language and governmentality by understanding affect as a discursively produced register that serves to legitimate the distribution of resources. I follow the role affect plays in constructing linguistic minority subjects as agents of globalization. I flip cultural entrepreneurs' understanding of themselves as liberal agents of linguistic change and show how they are constrained by the political salience of monolingualism. I draw on ethnographic fieldwork carried out in the field of linguistic minority cultural production in Acadie to track moments when questions of ownership appeared. I pay attention to the role affect played in navigating the tensions between the economic value of multilingualism for global markets and the remaining political salience of monolingualism for minorities. Affect served to reproduce the minority speaker as a particular type of subject, one "attached" to a community constructed as ideally monolingual, either in the past, present, or future. I then map out global linguistic minority governmentality to show how knowledge production on language is embedded in the tensions experienced by linguistic minority cultural producers.