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‪This article looks at how home education, in the French context, tests the definition of the “fundamentals” of education, in particular in the context of the “common core” (or socle commun), through the practices and representations of the actors responsible for inspecting and regulating them. From a series of thirty-one interviews with home education inspectors, three types were identified, corresponding to specific academic or professional trajectories. The first, “republican inspectors”, tries to be as close as possible to the institutional definition of fundamentals; a second type, “inclusive inspectors”, redefines the fundamentals around social connections; a final type, “child-centred inspectors”, more often recognise and value family expertise and underlines the specificity of each child.