The ECS doesn't have Na(l) or F(l), so in the solution with molten NaF, shouldn't water be oxidised and reduced whilst in the aqueous solution, F^-1 gets oxidsed and Na^+1 gets reduced?
Molten NaF does not contain water, that is the point of using molten. The ECS technically does not apply for this reaction since it won't be in standard conditions, however, they are not Na(l) and F(l) form due to still being in ionic form.
For the aqueous solution, the strongest oxidant gets reduced and the strongest reductant get oxidised. Since water is both a strongest oxidant and reductant than both Na+ and F-, it will react with itself.
When predicting redox reaction, it is always best to start circling what you have in your solution. In this case, we have H20, Na+ and F-. Since H20 is the highest reactant on the left side ( at -0.83V) and the lowest in the right side (+1.23V), it would undergo a redox reaction by itself.
You should have covered similar stuff in class using molten NaCl(l) which behaves in the same way.
Does any of that help any more?