How effective were the forces of the French Provisional Government compared to the other allies?

There is a Wikipedia article which gives an outline of some of the milestones in the evolution of the French military throughout World War II which provides a useful historical context for the development of the French Army as it existed in the post-Liberation period in question.

Corps Expéditionnaire Français (CEF)
A useful starting point in answering this specific question is to understand the reformation of the French Army which occurred on 1 August 1943, after the liberation of French North Africa, when the Free French Forces merged with the Army of Africa to form the new French Expeditionary Corps (Corps Expéditionnaire Français, CEF), under General Alphonse Juin. Juin was regarded as a very capable leader and the CEF performed very creditably during the Italian Campaign. By April 1944, the CEF was composed of 112,000 soldiers, including 60% Maghrebis (mostly Moroccans) and 40% French (mostly Pieds-Noirs).

The American General Mark Clark paid tribute to the French forces under his command in Italy in a letter to the French commander where he stated:

For me, it has been a deep source of satisfaction to see how the vital part played by the French troops of the Fifth Army throughout our Italian campaign against the common enemy has been universally acknowledged. During these long months, I have had the real privilege of seeing for myself the evidence of the outstanding calibre of the French soldiers, heirs of the noblest traditions of the French Army. Nevertheless, not satisfied with this, you and all your people have added a new epic chapter to the history of France; you have gladdened the hearts of your compatriots, giving them comfort and hope as they languish under the heavy and humiliating yoke of a hated invader. The energy and utter disregard for danger consistently shown by all members of the C.E.F., along with the outstanding professional skills of the French army officer, have aroused admiration in your Allies and fear in the enemy. From the banks of the Garigliano where your first successes set the tone which was to characterize the whole offensive, then pushing on to Rome through the mountains, crossing the Tiber and pursuing the enemy relentlessly to Sienna and to the hills dominating the valley of the Arno, France’s soldiers have always accomplished everything that was possible and sometimes even that which was not...With my deepest gratitude for the tremendous contribution that you have made to our joint victories, my dear General.

Forces of the Gouvernement Provisoire de la République Française (GPRF)
For their participation in Operation DRAGOON, the invasion of Southern France in August 1944, the French forces were formed into French Army B, under command of General Jean de Lattre de Tassigny, which on 25 September 1944 was redesignated as French First Army. By this time the French Army consisted of 560,000 regular soldiers and 300,000 irregulars of the French Forces of the Interior (FFI), former resistance fighters who had been brought under formal military command after the Normandy invasion. The FFI had numbered just 100,000 in June and had rapidly grown to over 400,000 by October 1944 when it was amalgamated into the regular French Army, creating a force of 1 million men by the end of 1944. By the end of the war in Europe (May 1945), French forces comprised 1,250,000, including seven infantry and three armoured divisions fighting in Germany.

The rapid expansion of the French forces after liberation, and the political difficulties resulting from the need to amalgamate large numbers of irregulars had a profound impact on the performance of the French Army in the field. The Wikipedia article describing French involvement in the Battle of the Colmar Pocket in the winter of 1944-45 outlines some of the difficulties:

On the part of the French, their replacement system was limited by the amount of training infrastructure they had been able to re-establish since reentering France in August 1944 and was further strained by a controversial French decision to "whiten" the French forces in Alsace by sending experienced Senegalese and other colonial troops — exhausted from fighting in Italy — to the south and replacing them with French Forces of the Interior (FFI) troops of varying quality and experience. While the FFI troops were capable of defensive operations, they had to undergo a steep learning curve in order to become effective at offensive operations, particularly where complex activities such as combined-arms operations were concerned.

Thus, at the close of November 1944, the French First Army deployed two kinds of units—highly experienced colonial units and "green" units that had recently received a large influx of FFI troops. Coupled with a supporting arms structure (artillery, engineers, etc.) that was weaker than that of other Allied field armies, the sag in French First Army troop proficiency allowed the Germans to hold the Colmar Pocket against an unsuccessful French offensive from 15–22 December 1944.

_{French and US forces meet during the Battle of the Colmar Pocket in 1945}