The classical definition of a statement, as I understand it, is that it is a declarative sentence with all indexicals resolved. So, as a statement,
a fluent is a statement schema such that resolving its temporal indexical produces a statement. (If we move on to propositions, we get into some deep issues, such as whether or not any propositions can change their truth values over time.) In other words,
a fluent is a family of statements all identical except for the point or period of time associated with them.
Sounds like an interesting concept. More generally, we can conceive of a statement-family as a statement schema in which one or more indexicals
are not resolved -- place, time, person, perhaps even propositional attitude.