The importance of the decision by Reynaud to fight on isn't what happens to Paris, it's that the French government moves to Algiers and continues the fight from North Africa.
When it looked like France was going to lose the war, France sent much of its air force to North Africa to keep it intact, rather than lose it in futile fighting. At that point, France had internalized defeat and was looking at the ways it could best retain as much strength as possible in a future German-dominated Europe. In any scenario where it fights on, France will make very different decisions.
In this case, France will have a substantial air force, its entire navy, and likely be able to evacuate a decent amount of infantry from France into North Africa. France can probably still field an army of around 500,000 to 1,000,000. The gold reserves of both France and Poland at Dakar are available to the Allies. France will still have lost almost all of its manufacturing capability, but US Lend Lease will likely happen earlier and both supply the French Army with any needed equipment and serve as means to industrialize French Algeria more. France will lack a manpower pool of white Frenchmen, but it has access to plenty of black colonials to raise reinforcements or even new formations.
With the French Fleet still active, it will neutralize Italy's fleet and allow Britain more strategic flexibility. The Battle of the Atlantic will turn in favor of the Allies more quickly. Italy will be eliminated from Libya by end of 1940 or Spring 1941 at latest. By end of 1941, the British and French likely have taken Sardinia and Sicily. If Germany still invades the Soviet Union (something I still find likely ITL), then an invasion of Italy in mid 1942 is even possible. After this point, what happens next depends on what other things you think will have happened between 1940-1942.
As for Paris in 1940? The Germans likely surround the city with infantry divisions as the panzers continue to push south. I don't see the Germans attempt to storm Paris until the Allied field armies are driven out. Then weakened by blockade without supply for several weeks, Paris likely falls quickly. Unlike the situation in Stalingrad or Leningrad, there aren't any food supplies coming. There's damage to the city of course, but I don't see Paris being completely ruined. Any commander in Paris at that time would be perfectly justified in surrendering the city to save civilian lives.