Copying my comment from a couple of days ago.
In fairness, July and August weren't inserted, they were renamed from Quintilis and Sextilis, literally the fifth and sixth months of the Roman calendar.
Much earlier, Pompilius (history about whom is largely legendary, and actions attributed to him should be taken with a grain of salt) introduced January and February and set the numbering out of line. These months were previously just lumped in as monthless winter days.
All Julius Caesar did was rebalance the calendar without changing the months. The rename of Quintilis wasn't even until after he was stabbed.
Gregory XIII then further tweaked it to give us the modern calendar.
