The development of open science requires a cultural change in academic institutions, including the acquisition of new knowledge and skills in fields like open access publishing, research data sharing and citizen science. The paper presents results from a survey on PhD training programs related to open science in ten highly ranked and research-intensive French universities. Based on the discussion of the empirical survey results (content, format, discipline, etc.), the paper establishes a list of some recommendations that may be helpful for the assessment of existing programs and for the development and implementation of new programs.