Academic research on measures of online influence has gained new impetus with the emergence of the Twitter social network. Indeed, Twitter materializes data (number of followers, number of posted tweets, number of retweets, etc.) that, depending on the definitions and concepts used, can be likened to a “diffusion”, “visibility”, “audience” or “influence” index. We propose to interpret this data as indexes measuring the audience of accounts. An account’s number of followers corresponds to the potential number of accounts likely to see this account’s posted tweets in their timeline; a message’s number of retweets indicates at the very least the number of times a message has been read and shared. Each Twitter account can therefore be measured in terms of its own audience. We analyse the distribution of this audience across the various accounts that make up the social network and we explain the mechanisms for building a large audience on Twitter. We specifically focus on French accounts that somewhat regularly post political tweets, that is, messages referring to the political sphere and its actors, institutions and activities. Our empirical analysis of the French political twittersphere supports the hypothesis of a trend towards an oligarchic concentration of hubs spreading political signals on the network. In order to scientifically analyse the social network, we created a panel including the 1,116 accounts with the largest audience in the French political twittersphere through the classification of a comprehensive database of 147,420 accounts that we ranked according to an audience index. Analysis of the Twitter audience panel reveals that only about a hundred accounts draw the bulk of the audience on the social network, and that these accounts belong to major media outlets or to figures holding top positions in fields that receive extensive media coverage. One of the main findings of our research concerns the extreme audience concentration even within the “Twitter audience” panel which includes the accounts which have the largest audience of the French political twittersphere. 29% of the accounts that make up the Twitter audience panel belong to journalists or media figures, 18% belong to media outlets and 14% belong to politicians. Most of these figures therefore come from media-covered fields and generally hold top positions in these fields. Also, the greater these figures’ media fame capital, the greater their chances of being at the top of the audience panel. In other words, the audience of figures on Twitter is directly correlated with their level of media fame capital.