In the last few decades, new discoveries have pushed the beginning of the biface-rich European Acheulian from 500 thousand years (ka) ago back to at least 700 ka, and possibly to 1 million years (Ma) ago. It remains, however, unclear to date if handaxes arrived in Europe as a fully developed technology or if they evolved locally from core-and-flake industries. This issue is also linked with another long-standing debate on the existence and behavioral, cognitive, and social meaning of a possibly chronological trend for increased handaxe symmetry throughout the Lower Paleolithic. The newly discovered sites can provide a link between the much older Acheulian in Africa and the Levant and the well-known assemblages from the later European Acheulian, enabling a rigorous testing of these hypotheses using modern morphometric methods. Here we use the Continuous Symmetry Measure (CSM) method to quantify handaxe symmetry at la Noira, a newly excavated site in central France, which features two archaeological levels, respectively ca. 700 ka and 500 ka old. In order to provide a context for the new data, we use a large aggregate from the well-known 500 ka old site of Boxgrove, England. We show that handaxes from the oldest layer at la Noira, although on average less symmetric than both those from the younger layers at the same site and than those from Boxgrove, are nevertheless much more symmetric than other early Acheulian specimens evaluated using the CSM method. We also correlate trends in symmetry to degree of reduction, demonstrating that raw material availability and discard patterns may affect observed symmetry values. We conclude that it is likely that, by the time the Acheulian arrived in Europe, its makers were, from a cognitive and motor-control point of view, already capable of producing the symmetric variant of this technology.