Yes and No - Because the idea of constitution as we know it today is western. Hindu society should follow rules based on Hindu scriptures. There is a hierarchy of the main scriptures with revealed texts being the most authoritative These scriptures are Vedas and Tantras. Shaiva Agamas and Vaishnava Samhitas are also considered revealed texts by different sectarians.
Second is "Fifth Veda" or Itihasa and Puranic texts. These are not revealed texts but have sanction from mantra and other portions of Vedas. They were written by Vyasa, except Ramayana which was written by Valmiki under the blessings of Mata Sita. Some Puranas are said to contain blemishes and are classified based on Gunas. Shaiva scriptures consider Vishnu and his puranas Tamasic, and vice-versa. Some Puranas are claimed to be better than all others, and a few are claimed equal/superior to revealed texts like the Kalika Purana. Itihasa also is claimed to be equal and superior to Vedas. But overall, they are #2 since they are not revealed.
#3 is Smriti. These are semi-sacred, remembered scriptures. Although the words of Manu have Vedic sanction, it is not referring to Manusmriti since this was not authored by Manu himself. Smritis or remembered texts are to be discarded if they go against revealed texts and Fifth Veda.
So yes we should definitely use Smriti rules for society if they do not contradict other sacred scriptures. It also depends on which sect you are following. It is debated which smriti should be considered best for the present age or Kali Yuga