Fundamentally, they just didn't have the time to do it when it became clear that the Germans were going to seize the ships.

Warships of the time generally were not powered by internal combustion engines or gas turbines, where you could just turn the ignition key and get going. They were generally fuelled by steam produced by boilers. It takes time to get a head of steam up. In peacetime, the snipes (engineers) are usually starting the process about a day before the ship is due to leave, and this would continue all the way to the decomissionoing of the oil-burning steamers. In emergency situations, one can risk damage to the system and do an emergency startup. That'll still take about two or three hours, depending on the ship. Some submarines, with instant-on diesel engines, did make a break for it and head for North Africa.

Case in point: When the Germans came around the corner to raid the base at the Falklands in WW1, it took just over two hours between when the 'Enemy in sight' signal was given until when the first ship slipped her moorings. Nevada must have broken all sorts of records and safety rules in order to get underway in 40 minutes at Pearl Harbour. When the Germans started entering the port, the ships's crews needed to delay them long enough to set the scuttling charges, let alone get up steam. Even at that, it's possible that the German soldiers didn't realise how short a time it could take to scuttle a ship, they seemed rather slow and methodical about the whole thing, being held up at the gate by a request for paperwork (and being under instructions to avoid bloodshed if possible). When they forced the issue, they reverted to 'combat troop' mode and methodically eliminated resistance from the defending French sailors, instead of beelining to the ships.

That said, there was some political dithering at the higher levels. There was some debate as to whether the ships should sail or not before the Germans made their run for the port. No such order ever reached the fleet, and the French had this terrible tendency not to do anything without orders from duly appointed superiors. It resulted in the fall of France in 1940, and several days of shooting in North Africa against the British and Americans. The French Admiral (Darlan) in North Africa who was now working with the Allies had attempted to order the Toulon fleet to move to Dakar, but the response from the fleet commander, Laborde, who viewed his chain of command as coming from Vichy, replied with an invective.

So, yes, the fleet probably could have been moved had there been a will to do it before the Germans made their attempt to seize it. But once the attempt had started, scuttling was the only practicable option.