We want to buy a property with my partner and his/her grandmother. My partner and I would acquire the bare ownership of the property and the latter’s grandmother the usufruct. In order to determine the rights of each on the propety(...)

...are we bound by the tax scale of article 669 of the general tax code ?

No. The purpose of this scale is to determine the respective values of usufruct and bare ownership for the calculation of the duties due in regard to the tax authorities. It does not impose itself in civil matters (Cass. Civ. 1e, 25 Feb. 1997, n°94-20.785). The parties can freely set the value of each of the divided rights. However, it is recommended to use an economic evaluation to be as close as possible to the real value of each of the rights.