‘It’s’ is a contraction of ‘it is’ or ‘it has’ – a less formal version of those expressions. As an example, the following sentences have identical meanings:
It is expected that visitors to France try to speak French.
It’s expected that visitors to France try to speak French.
‘Its’, on the other hand, is the possessive form of ‘it’.
Like its people, France is French.
Note that this differs from the way you would show possession for a person or known entity (e.g., France’s language, Campbell’s bike).