What law established the constitutions of towns and cities in Italy?

The Lex Iulia Municipalis is the correct answer because it specifically addressed the administration of municipalities in Italy and established the legal framework for their constitutions. Enacted in 45 BCE during the period of the late Roman Republic, this law provided guidelines for the governance and organization of towns and cities, including their local government structures and citizenship rights. This was significant as it aimed to promote local autonomy and allow these communities to develop within the broader framework of Roman law and governance.

The other options refer to different laws with distinct purposes. The Lex Agraria primarily dealt with land distribution, particularly addressing land for veterans, while the Lex Papiria was related to financial and legal procedures in a different context. The Lex Fufia Caninia focused on the treatment and rights of slaves and manumission, which does not pertain to municipal governance. Thus, the Lex Iulia Municipalis is uniquely suited to the question regarding the establishment of constitutions for towns and cities in Italy.