The French team got into Madison Square Garden through a massive underground burrow from the subway system and immediately encountered Godzilla eggs. Even if they had managed to block the doors leading out of the Garden, what was to stop the baby ‘zillas from getting out through that tunnel?
Initially, there wasn't any real reason to leave. The babies had lots of fish or soldiers to distract them. They probably would have left, given more time, but the USAF fried the entire nest pretty quickly.
