The first ripple of the absence of Napoleon will come at Toulon. Without Napoleon, the siege will probably get longer although I doubt the city would be able to resist. But even if the city stays in Royalist hands, I'm pretty sure it is of few consequences.
Westphalian said:
If you believe the Bonapartist view of history, then on 5 october 1795, a royalist uprising will topple the directorate, while the Count of Artois marches from the Vendee on Paris.
I'm not sure Charles of Artois (later Charles X) would need to march on Paris from Vendée... If the Directorate is overthrown and Paris falls to the uprising, I'm pretty sure it's game over for the French Republic. That being said, it isn't sure that the Royalists would suceed in their uprising of the 13 Vendemiaire an IV. Barras might still be able to find a general competent enough to bring down the uprising.
The problem comes after that date... Would there be an Italian Campaign? Napoleon was one of the main advocates of that plan since 1794 OTL: without him, there is no guarantee the Directoire would consider it. If he does, the question is: which commander would be chosen and of what caliber is he compared to Napoleon? Some people like to think Hoche or Moreau were of the same caliber (I personnally doubt it) but there is no guarantee the first would be chosen (I believe he was occupied elsewhere although I'm not sure) while the second was leading the armies in Germany during OTL First Italian Campaign. Then comes the question of the level of success achieved by said general in Italy: there are few chances he is as successful as Napoleon. Considering all of this, there are high chances the Republic is in a worse military situation without Bonaparte.
We also have to consider the weakness of the Directoire: in 1797, the Republican Assemblies found themselves with a
Royalist majority. Of the five Directeurs, two were Royalist and two were Republican: the fifth one, Barras, was a key-figure of the Regime and he was hesitating. What led him to take a side OTL was that Napoleon arrested a Royalist agent (the Comte d'Antraigues) who had documents proving the treason of Pichegru, the leader of the
Conseil des Cinq Cents (one of the two assembly). The result was the coup d'état of 18 Fructidor an V (September 4, 1797): elections were annulled and the armies of Hoche and Augereau (the latter being sent by Napoleon) helped the coup succeed. Without Napoleon, d'Antraigues might not be arrested and thus Pichegru's treason might not be discovered. If so, Barras might not take the Republican side and I'm not sure the other Directors have enough power to stage the coup. If so, the Monarchy can potentially be restored from that moment on.
In other words, no Napoleon probably means the French Republic is in a far more difficult position than it was OTL.