A cursory web search tells me shutters can influence the DPE ("diagnostic de performance énergétique".) A bad rating means you can't rent your property.
There’s definitely a cultural or historical component. In my experience shutters are extremely common, near universal, in southern Europe but much less so in northern. Which is a shame because a modern PVC roller shutter, well installed and with insulated slats, also does wonders in winter.
https://immobilier.lefigaro.fr/article/seulement-54-de-logem...
From a quick search, older versions of the DPE ignored shutters, modern ones take them in account and their effect ranges from neutral to positive depending on details (materials, insulation, fit). It’s not entirely clear if both high seasons are considered (insulation and fit I’d think a lot less critical in summer).