Let's grab a book, shall we? Let me begin by saying that I was wrong saying there were no regular army units in Paris.
The 53rd, 62nd, 7th, 89th, 94th, 96th, 98th, 99th and 101st were Germans and had
skyblue coats; the 63th-66th, 69th, 76th, 85th-88th, 92nd, 95th, 97th and 100th, red coats, the men being either Swiss or Irish. All Swiss regiments were disbanded in 1792, and additionally the 101th Royal-Liégeois left the country almost entirely in the same year. The light infantry, 12 battalions of them in 1789, wore green.
The only unit wearing
darkblue was the National Guard, who wore
this uniform. The National Guard, however, was pretty pro-Revolution (Technically they stormed the bastille), besides being organized officially only one day prior to the storming of the Bastille. Additionally, one of the 'Guard' regiments, The Gardes-Francaises joined the revolutionaries, who also wore these
dark blue uniforms - Of serious different design then those shown in the game. The other guard regiment was the Swiss Guard, with the famous red uniforms, who stayed loyal to the end.
There were a couple of deserters from other regiments but they wore the white uniform of the standard line infantry. The regular army did not take the dark blue uniforms of the National Guard until 1792, with the abolishment of the monarchy and the start of the war of the First Coalition. Let's not forget that France was a constitutional monarchy for three years (well sorta).
Garrisoning the Bastille were Swiss line soldiers (red uniforms) and a Veteran company - No idea what they wore. The Revolutionaries also never actually took the Bastille - They only took the undefended outer plaza and then they played the waiting game, until the garrison commander gave up and ordered the drawn-bridge lowered.