Scholars in the discipline of international entrepreneurship have mainly studied rapidly internationalizing firms. However, the majority of entrepreneurial firms are family-owned businesses (85% of all firms in the EU and the USA). Research on family business has focused on the importance of bonding social capital whereas, despite its importance, bridging social capital has not so far attracted much attention. It has been argued that bridging social capital plays an important role in firms’ internationalization processes. The purpose of this article is to examine the role of bridging social capital in the initial entry and post-entry operations of eight family SMEs with regard to the French market. We found that in foreign market entry social capital generally had a serendipity role, based on weak and intermediary relationships. In the post-entry situation, the role of strong and formal ties emerged strongly, and social capital most commonly took on efficacy or liability roles. Thus, it seems that the social capital of family entrepreneurs is limited to their strong bonding social capital, and perhaps to their strong national social capital. However, when such firms start to internationalize, they have to find new networks to gain the bridging social capital that will enable foreign operations. It seems that having a limited number of international ties drives family SMEs to search for relevant contacts at international trade exhibitions and trade fairs.