Does the System F with pairs have the strong normalisation and subject reduction properties?
The treatment of pairs given by encoding, such as that in Proofs and Types, isn't what you usually want since they aren't "surjective pairs", i.e., there is no eta rule.  Let's call surjective pairs, products.

An extension of system F with products and unit is given in: Di Cosmo, 1995,  Isomorphisms of types: from lambda-calculus to information retrieval and language design,  Birkhauser: Basel.