The French Government has now produced a form to be downloaded and completed each time someone leaves home (from noon today). Comprises tick boxes with valid reasons that you're out and about. Travel between home and work, out buying essential items, health related visit, assisting of elderley / vunerable or for brief physical activity local to home. The form includes name, DoB, residence, signature and time and date.
Persons out without a valid reason are liable to fines of € 38 or € 135 (I haven't sussed why there are two different fines)