I understand that military units remained in-action in their foreign regions, like Africa, and were used by the Aliies. By 1945, newly-trained units were already closing in on Austria with the U.S. and British forces.
By VE Day the French armed forces in Europe could muster twenty divisions, the best of which were the three armored divisions and five infantry divisions of the First Army that had invaded Germany under the command of Jean de Lattre de Tassigny. The First Army was part of the US supply chain and under the overall command of General Jacob Devers's Sixth Army Group. The rest of the French Army consisted of second-rate divisions that had been formed recently from FFI manpower and which were employed in Germany as occupation troops, along the Alpine border with Italy, and to besiege the pockets of German resistance which remained in Atlantic ports like Lorient and Saint-Nazaire. There was also a division raised to fight Japan in the far-east, but the Pacific War ended before it could be employed. If the war against Germany had continued for longer, more divisions would have been raised to constitute a Second French Army for the Western Front. Compared to other liberated nations, the amount of men and material France could put in the field in 1945 was truly impressive.
How were they able to do it? First and foremost, through the lend-lease of Allied (mostly American) equipment. However, this wealth of military aid, and the opportunities to use it, would never have come without the inflexible insistence by Charles de Gaulle that France be treated as an equal Allied power rather than a liberated nation, nor without the capable manpower supplied first by France's African colonies, and later by the French Forces of the Interior in metropolitan France.