The Akatsuki members might see Gojira as an opportunity. They could try to capture it or use its power for their own evil purposes. Itachi, if he were still around, might try to stop them from doing something stupid that could lead to even more destruction. Naruto would have to not only deal with Gojira but also fend off the Akatsuki's attempts to use the situation to their advantage.
Sakura would probably be terrified at first. She might initially think it's a new kind of giant summon gone wrong. But then she would gather her courage and try to help Naruto deal with the situation, maybe using her medical skills to heal any injured people in the chaos. Kakashi, on the other hand, would be very calm and start observing Gojira's behavior to figure out a strategy.