Final answer:
The National Convention wrote the second constitution, transforming the French government into a Democratic Republic and abolishing the monarchy.
Step-by-step explanation:
The governing body that wrote the second constitution, changing the French government to a Democratic Republic and ending the monarchy, was the National Convention. The National Convention was a representative body composed of various groups of revolutionaries with conflicting opinions. It was established after the suspension of the king by the newly formed Legislative Assembly and played a pivotal role in convicting and executing Louis XVI.