The French during the First World War were not weak, not even somewhat. Most assumptions about France's military weakness during the First World War comes from their performance during the opening months of the war, during the serious of clashes we collectively call the Battle of the frontiers which culminated in the First Battle of the Marne, the battle that checked the German advance towards Paris.
France's performance during this period was admittedly quite poor but it wasn't because they were militarily weak, it was because their doctrine at the time emphasised offensive action at all time. French analyses of their French defeat during the Franco-Prussian war fifty years earlier had come to the conclusion that the armies hadn't been offensive enough, that they had repeatedly ceded the initiative to the Prussians allowing the enemy to outflank and outmaneuver the French formations. Pre-war planning for a future conflict emphasised that the French should attach, always attack. You may have heard of the term cult of the offensive, this was an ideology instilled in all French soldiers and was enacted on the Franco-German border when the First World War began. The French were relying on mobility and rapid firing artillery to secure them command of the battlefield. The Canon de 75 modèle 1897, the famous French field gun of the war, was designed and developed specifically to achieve this. Light weight, mobile and capable of firing fifteen rounds a minute, the 75 was intended to support the rapid and aggressive advance of the French infantry and keep moving forward.
When the French launched their attacks in 1914, the Germans initially just held their positions. Their goal was to simply hold the attention of the French while the advance through Belgium was underway. The successful advance through the Low Countries was intended to allow the Germans to get behind the main French force and strike at Paris, capturing the capital and forcing the capitulation of the French before the Russians could mobilise in the east and threaten thinly defended east Prussia. The Germans knew that one of the first things the the French would do in the event of a war was to recapture the lost regions of Alsace and Lorraine, those regions ceded to Germany at a condition of the French surrender fifty years earlier. This was exactly where the French advanced in August 1914. That said, the capture of territory was not France's primary objective. Joseph Joffre, the French commander, wanted, primarily, to bring the German forces to battle and defeat them by outmaneuver in the field. What the French found however was that they were outgunned, severely.
The French 75 was a very good gun, quite remarkable in its capabilities but it was a field gun. Like the cannons used masterfully by Napoleon Bonaparte, the 75 was designed to accompany the infantry into battle. Firing over the heads of the advancing French infantry, the 75 had to be located relatively close to the battlefront. The Germans also had field guns, the 7.7cm FK 96 n.A., and while these had a lower effective range then the French 75s, the Germans also had heavy artillery. The French did not. To maintain mobility, the heavy artillery was not placed within the French Corps, the French didn't even really have any heavy artillery except for those guns stationed within their forts. So the French attack, the infantry go forward into Alsace, the 75s fire in support and then the Germans counterattack. Crown Prince Rupprecht, the commander of the German army in Lorraine, is given permission to counter the French. He does so and the heavy artillery of the German army. Outranging the French guns which were positioned in the open, the French 75s are outmatched, forcing the gun teams to withdraw or be destroyed, leaving the infantry unsupported and subjected to the German field guns. This led to massive French casualties and forced the French armies to withdraw. This was a result of a doctrinal failure, not an indication of military weakness.
The strength of the French military during the war is plainly evident. Not only was France able to sustain the tremendous losses it suffered during the Frontier battles, the Battle of the Marne and the offensive actions of 1915 (including suffering more casualties at Gallipoli then the ANZACs did), they also managed to fend of the Germans at Verdun, the longest battle of the war. There is no argument that three years of fighting didn't have an effect on the French army, the 1917 mutinies attest to this but again, this was not symptomatic of French weakness, it was a symptom of the circumstances and conditions the French were forced to respond to. Verdun created a psychological scar within the French army and few formations didn't suffer from it thanks to the policy of rotating formations through the sector to provide relief. The mutinies did not signify an unwillingness of the French soldiers to continue fighting, they were content to defend their positions but refused to undertake offensive actions. Simply put, the French soldier had lost trust in their commanders. That the french emerged from 1917 with an incredibly effective army, capable of undertaking massive offensive actions such as the Second Battle of the Marne and the Meuse-Argonne Offensive clearly shows that the French army was anything but weak.
Throughout the war, the French military had demonstrated the capability to sustain enormous losses, learn from past mistakes, develop new tactics and doctrines and reform its leadership when necessary. During the crisis of the 1918 German Spring Offensive, it was a French General, Ferdinand Foch, that was appointed generalissimo of the Allied forces. Had the British or the Americans considered the French to be militarily weak, they never would have trusted such a pivotal appointment to a French officer. The French were not weak, they were, as were just about every other belligerent, unprepared for the reality of industrial warfare but just like every other belligerent, they adapted and ultimately emerged victorious.
Sources:
The First World War by John Keegan
Pyrrhic Victory: French Strategy and Operations in the Great War by Robert Doughty
The Ideology of the Offensive: Military Decision Making and the Disasters of 1914 by Jack Snyder