There's a very big difference between war caused debt and economic caused debt (note that I'm basically making these two "debts" up, and things are more nuanced obviously, but I'm going to ignore the nuances for now, these are very broad strokes.) When you come out of war, you're either the loser or the victor (one way or another, there are very few true "ties" in war.) And while capital may be destroyed in both cases, an economic crises doesn't necessarily leave your physical infrastructure and entire social system completely unrecognizable.
Further, Piketty seemingly completely ignores the Marshall Plan and all that it included in rebuilding Europe. And yes the Marshall plan was a form of debt forgiveness, but as a huge portion of the European continent was a smoking crater, things were different in 1945 than Greece in 2015.
Further, some historians/economists will argue that the "German miracle" (and "Japanese miracle" as well) were in part because of the destruction cased by the wars. With all the manufacturing capabilities destroyed, they were able to rebuild with the latest and greatest technology of the time. (and if you take this further, as the US was able to rest on it's un-destroyed capital equipment and make huge profits during the rest of the 1940's, 50's and early 60's, and never re-invested as Germany and Japan were forced too, this eventually lead to the downfall of the US Industrial might, in part.)
Personally, I think this has more to do with his French nationalism than anything else, at least as it appears to me in the interview.