A body of literature shows the destabilizing role of ICT in the cultural industries in general, and in press industry in particular. This literature demonstrates that constant experimentation and innovation in the area of organizational arrangements and business models (BM) has become a key competitive advantage. As a result, traditional BMs, which were dominant and stable in different cultural industries (such as media, film, music, publishing etc), have given rise to a multiplicity of arrangements in business management and the emergence of disruptive and innovative business models, which often successfully coexist in the same market segment. According to this view point, strategic and structural change is necessarily driven by competition or the need for efficiency. However alternative theories predict that, depending on the industry structural characteristic, only early adopters of innovation may be driven by a desire to improve performance. When an innovation spreads and organizational field becomes more established, there may be a push towards strategic homogenization. We argue that the case of the French press is quite symptomatic of that standpoint. From the empirical analysis of 100 press websites observed over the period from 2004 to 2014, the paper substantiates the convergence process towards three dominant clusters of online BMs: "A minima Digital", "Pure Players" and "Exploring Leaders". Using a Probit econometric model the paper puts forward that this isomorphic process is mainly due to the fact that mimetic behavior over-weights search for performance in French press.