Much existing social commentary and scholarship around the regulation of the European digital economy is focused on how societies could better regulate that economy and its associated harms. Such analyses often portray a problematically viewed order as ungoverned, or not effectively governed, by law. Instead, I argue for more (re)descriptive analyses on how our pre-existing legal structures powerfully create order in the European digital economy. I explain why we should explore the productive connections between pre-existing European legal arrangements and socio-technical order, and discuss what such exploration could entail. The article covers three complementary ways in which legal arrangements are productively connected to sociotechnical order: as tools of ordering to address problems and promote values; as tools that can also enable projects unintended and unforeseen by policymakers; and as constitutive of technologies and other forms of order. It provides concrete examples of these productive connections from various contemporary struggles within the governance of the European digital economy. I argue that focusing on the analysis of productive connections may shed light on how pre-existing legal arrangements are baked into and shaped by the European socio-technical order. As the current order of the European digital economy is characterised by massive inequalities, these analyses can also direct our attention to how our pre-existing legal arrangements can produce and reproduce inequalities and oppression. Analyses of pre-existing legal arrangements might produce different attributions of responsibility and possibilities of contestation than analyses of legal deficiency.