What did the French government do with the massive amount of corpses?
They were buried in mass graves in various cemeteries around the city. Trenches were dug, and during the height of the Terror they were covered with a sort of wooden lid with doors. The planks were meant to keep the smell in, and when bodies were transported there with carts, the doors could be opened to get the bodies into the trench.
Which grave you ended up in depended on what date you were executed on. The people living nearby complained, and worried that the presence of so many dead bodies would spread disease, so the bodies were taken to new parts of the city every few weeks.
The bodies were sometimes stripped, and the Paris commune ordered that police would be present at the burial to prevent this. After being placed in the trench the bodies were covered in quicklime to speed up the decay.