You have heard correctly. France did have a manpower shortage in WWII, more or less directly as a result of WWI. That said, I would like to point out that this can sometimes be exaggerated, as it might have been in your case, and the circumstances of France's low manpower exceeds just WWI casualties and a stagnant birth rate. Also, as far as my knowledge is concerned, France's manpower was not the crucial factor in why France was defeated in WW2 either, and rather a complex net of mistakes and failures that deserve their own topic of dicussion.

That said, concerning the First World War, France definitely suffered heavy casualties in the war that resulted in some steep manpower shortage in the future. So many men died in the First World War that it's estimated that France, by the beginning of WWII in 1939, had 300,000 fewer men defend the nation than it had at the beginning of WWI in 1914. Among the lost were the unborn sons of the men that died in WWI, but France's manpower shortage was also badly exacerbated by the declining birth-rate that it had started to experience as early as the 1800's, and persisted until recovering after the second world war. As an example, during WWI, in 1915, the next class of men newly available for conscription in Germany was ~460,000 compared to only ~184,000 in France. This ratio (1:2.5) remained more or less the same all the way until and through WWII; there were two or three Germans for each Frenchman each year that were available for conscription.

Then consider the Political and Financial constraints of France that, again, did not compliment France's dwindling army. The political turmoil of the 20's and 30's in France saw Politics shorten the term of conscription service down to 1 year from 3 years. Staying in the Army after one's term of service was up was not exactly the most appealing option for most men either, as the political and cultural and nationalistic motivation of the Revanche has been fulfilled by France's victory in WWI, and the pitiful wages of the Army made a career in the military as an officer financially desperate. Finally, France hoped to supplement it's population deficit with colonial troops, but this was never fully fulfilled.

France's very large manpower shortage, combined with France's traumatic experience in WWI, were the main reasons for why the Maginot Line was built; the forts and defences were meant to capitalise on compensating for France's low manpower, among other things. The irony here is that, even though the Maginot Line did not statistically eat up that much of the military budget, it sapped resources and money from an already depleted army, leaving many technologies, strategies, and ways of thinking stagnated in the WW1 era.

Main Sources:

• To Lose a Battle: France 1940 by Alistair Horne
• From the Rise of Hitler to the Fall of Dunkirk: Blitzkrieg by Len Deighton