What should I say when I see the family in public?

What you say depends on if you’ve already had contact with them. If you attended the visitation or funeral, merely greet them warmly and ask how they are doing. If this is your first meeting with them since the death, your first reaction might be to express your sympathy. However, it is nicer not to bring up the death as this might evoke emotions that might be painful for your friend to deal with in a public place. Perhaps it would be better just to say you understand that this is a difficult time for them. You might even ask when it would be a good time to visit or go to lunch or dinner.