Few English translations can be scared up by an online search.
I have found one, which will be presented in this post.
However, a few caveats.
The translation does not match the ten verses from the OP.
There are only six stanzas in this presentation,
and the fifth English stanza is a translation of
a verse that does not appear in the version I presented in the OP.

This translation appears, with its brief introduction, in the biography
Eugène de Beauharnais: The Adopted Son of Napoleon,
author Violette M. Montagu, published in 1913.

"...but then, Napoleon had never ceased to be the soldiers' hero. There is a quaint old song, a mixture of German and French, dating from the Napoleonic epoch, which is still to be found among collections of folk-songs on the Continent, and which, if my readers will forgive me, I will reproduce, as it, perhaps better than anything else, shows the spirit that reigned among the Emperor's vieux grognards:

THE OLD WOODEN LEG

In France was I born, in France was I bred,
The home of fair women and wine.
My name is Jean Grillon, mesdames,
My pride is my old wooden leg.

Tobacco, fresh air and potatoes
Are all that an old soldier asks.
And if on his breast he wears the Cross
To his grave he will go with a smile.

Think ye that I love not the fair sex?
Then ye are mistaken, forsooth!
The old wooden peg may go lamely,
But the lips are still ready to kiss.

I laugh and I sing and full often
Crack jokes with my old wooden leg.
My pegs may be worn out with service
But the top of me's lively as aye!

So we hobble through life all undaunted,
Poor Jean and his old wooden leg.
Kings, emperors and princes are proud to house
Brave Jean and his old wooden leg.

When Death reads the roll-call of honour,
And the time comes to lay down my arms,
Saint Peter will utter the word of command:
"Make room for that old wooden leg!"