Seven new archeointensity data are obtained through the analysis of groups of pottery and kiln fragments from ceramic workshops unearthed in France, precisely dated from the High Middle Ages. The measurements are carried out using the Triaxe magnetometer, following a dedicated experimental protocol that takes into account the effects of anisotropy and cooling rate (CR) on thermoremanent magnetization acquisition. The new data are consistent with the evolution of intensity variations described by our previous data obtained in France and Northern Italy, which display between the 5th and 10th c. a pronounced camel-back shape. In particular, they provide supporting evidence of an intensity minimum that occurred around the transition between the 7th and 8th century. These data, combined with a selection of previously published results within a 700 km radius of Beaune and re-examined based on CR correction, formed the basis of new regional mean intensity variation curves based on two independent modeling approaches. The first algorithm developed by Thébault and Gallet (2010) based on bootstrapping and now irregularly spaced knots according to the data distribution gives rather smooth intensity variations, while the second approach proposed by Livermore et al (2018) based on a transdimensional Bayesian technique shows more abrupt variations with sometimes stronger amplitudes. We explore the dating potential of these two variations curves, which have an unprecedented resolution, by studying two medieval pottery workshops. Six fragment groups (three per workshop) are analyzed using the Triaxe protocol, providing mean archeointensity values for each of the two sites. Two different procedures are used for their dating, either by comparing the intensity value to be dated with the reference intensity variation curves obtained from the two modeling techniques or by analyzing the marginal posterior probability distribution of the age values derived from the method of Livermore et al (2018). For France, the two techniques yield very similar results. The archeointensity dating results combined with archeological arguments and radiocarbon data, make it possible to better constrain the age of the end of activity of the two workshops. Archeointensity investigation of displaced materials thus appears as an effective means to obtain original chronological constraints on the age of their production, paving the way for a wide range of complementary research on Medieval pottery.