There is no possible translation of “R’li r’lan r’lan tan plan
Tire lire en plan”; it’s just as what you find in “Little drummer Boy“, as reproduced below. However, as is suggested in the comments (jlliagre) a rendering might eventually be decided upon.

Pa ra pam pam pam
Ra pum pum pum,
Ra pum pum pum

A longer extract from that song shows that this is not translated.

Come they told me
Venez ils m’ont dit
Pa ra pum pum pum
A new born king to see
Qu’un nouveau-né roi est à voir
Pa ra pum pum pum
Our finest gifts we bring
Nos plus beaux cadeaux nous apportons
Pa ra pum pum pum
To lay before the king
Pour poser devant le roi
Pa ra pam pam pam
Ra pum pum pum,
Ra pum pum pum

Very probably “R’li r’lan r’lan tan plan” has been made up to reproduce the sound of drums; as we find an R-sound in sound of the drums for “Little Drummer Boy” we also find one in the mimicked sound of the drums in this revolutionary song.

“Tire lire” in “Tire lire en plan” has nothing to do with “tirelire”, that is “piggybank”; again, those words are merely words used for rhyming sounds.

I’m aware of no translation of the song, but I could make one up; here it is below.

Firmly forging ahead in triumph
The burgher at the sound of drums
Is marching to the Bastille
And everywhere is felt his ardour

(The burgher and the merchant
Are marching to the Bastille)

Citizens of all walks of life
Behind the flying colours
Are marching forth undaunted
Nothing cows them down

On all sides can be heard
The sounds of thundering brass
Aimed at the citadel
O! fatal Bastille!

Thou will before long
Thou will before long
Yield to the triumphant arms
Of your besiegers

Get out of your funereal dungeons
Victims of a detested rule
See through the darkness
Liberty’s rays
For too long gloomy sadness
Filled your hearts with poison
Bathe in tears of joy
Your liberators brow