To what extent did Verdun influence the policy-making of France and/or Germany
between the two World Wars

For France, it inspired the Maginot Line. Pity about the hole in the middle.

For Germany, it inspired the concept of the Blitzkrieg which exposed
the limitations of fortresses against the deadly combination of planes
& tanks.

For the record, Germany won.

Great, but could you elaborate a little on specifics of policy-making.
Ciao,

It gave France the illusion that she could rely on Treaties and
Alliances to enforce the provisions of the Treaty of Versailles to
contain the might of German industrialisation and secret rearmament.

The French illusion was progressively shattered after Hitler came to
power in 1933. The coup de grace (a word or two of French seems
appropriate) was delivered through the Ardennes in 1940 when German
forces poured through this supposedly impassable area.

C'est la guerre!

Here's a quote from the French Field Marshal following WW1:

"Airplanes are interesting toys but of no military value."  --
Marechale Ferdinand Foch, Professor of Strategy Ecole Superieure de
Guerre.

The British Earl Haig, same vintage, insisted that there would always
be a role for men with horses and swords.