I would disagree. An Improvised weapon is any object you can hold in your hand. The description of improvised weapon also gives specific examples of melee and ranged weapons being used as improvised weapons.
So you would be okay with the DM telling your greatsword wielding fighter to roll a d8 for improvised damage? I wouldn't. Weapons are by RAW not improvised weapons. They are weapons. The improvised weapon section says the following.
"Sometimes characters
don't have their weapons and have to attack with whatever is at hand. An improvised weapon includes any object you can wield in one or two hands, such as broken glass, a table leg, a frying pan, a wagon wheel, or a dead goblin."
The "any object" portion is not in isolation. It is in the context of the bolded. In proper context it means "Any object that is not a weapon."
The next paragraph just reinforces the first.
"Often, an improvised weapon
is similar to an actual weapon and can be treated as such. For example, a table leg is akin to a club. At the DM's option, a character proficient with a weapon can use a similar object as if it were that weapon and use his or her proficiency bonus."
It can't be similar to an actual weapon if it is an actual weapon. Similar = close to, not equal to. Then it gives examples of a table leg being SIMILAR to a club. It's not a club, but just similar to one.
The last paragraph reinforces the first two.
"An object that
bears no resemblance to a weapon deals ld4 damage (the DM assigns a damage type appropriate to the object). If a character uses a ranged weapon to make a melee attack, or throws a melee weapon that does not have the thrown property, it also deals ld4 damage. An improvised thrown weapon has a normal range of 20 feet and a long range of 60 feet."
It talks about the improvised weapon resembling or not an actual weapon.
At no point is the improvised weapon section applying to an actual weapon. The entire section is about when the characters don't have access to a real weapon and have to improvise one from something that is not normally a weapon.
So even if you rule that the flame blade is an object, which is viably ruled in either direction from the text, it still couldn't be an improvised weapon because it's a weapon.
Edit: As was mentioned in another post, if you use a weapon in a manner it is not intended to be used for, such as swing a sword by the blade and not the pommel or trying to hit with the pommel, that would be improvised. The flame blade used in that manner(if it's even ruled to be a solid object and not a shaped field of energy) wouldn't do full damage. It would do far less.