Demonstratives are from Cree, sometimes in a function similar to definite articles. They have different forms for the two genders (e.g. awa 'animate singular', uuma 'inanimate singular') and also in plural.
Definite articles are from French. They have different forms for the two genders (li 'masculine'; la 'feminine'; plural for both genders lii).
When a Cree demonstrative is used, a French definite article is also used.
On the other hand, it is not really definiteness or specificity that characterizes the use of li and la.