let me contribute some extra clues that might help you narrow your search down.
From the information you've just supplied we can draw some interesting conclusions as follows:
The French Army was not at war in 1804 when William was born BUT Napoleon did got to war again in 1805 and against a coalition of Britain, Austria and Russia. The major land actions of this 1805 campaign were against purely Austrian forces in Bavaria and then against a combined Russo-Austrian force at Austerlitz in The Czech Republic. This was not Napoleon's celebrated "invasion of Russia", that did not occur until 1812 but it did involve French and Russian troops while your William Goodman was still a baby. The next campaign involving French and Russian forces was in 1807 and was a campaign fought largely in Poland and then East Prussia. The casualties for the French Army were much higher during this campaign than they had been during 1805. There is then a break and France and Russian do not fight again until 1812. It was during the 1812 campaign that both the French (and Allies) and Russian armies largely annihilated each other in the snow - War & Peace, etc.
So, IF William's father died while he was a baby AND whilst fighting the Russians then really only the 1805 or 1807 campaigns fit the clues. This is good news because the smaller French army during these 2 earlier campaigns would be likely to be much better documented than the 1812 force.
Useful clues to narrow your search would be the town or area in France where the family lived. The French regiments were largely geographically based and once you know where Williams father was likely to have been recruited you could narrow the list of regiments to research. Obviously a name or a birth date, marriage date, dates would be useful in finding him. The family name - Goodman - does not sound French so possibly the fathers regiment was one recruited from foreigners, a long standing tradition in the French Army.