ก็ has no translation, which is why it vanishes from foreign Thai and why nobody misses it enough to mention. Its job is structural rather than semantic: it marks the second half of a two-part sentence as the second half.
ถ้า opens the condition. ก็ closes it and announces the consequence. French does this with word order and a comma, so there is no French word to attach the habit to, and it has to be learned as a shape.
- ถ้าฝนตกก็ไม่ไปtʰâː fǒn tòk ก็ mâj paj
if it rains then I won't go
Dropping it is not wrong, it is unfinished
The listener has been told by ถ้า that a condition is running and is waiting for the hinge. Leave it out and the sentence still parses, but it arrives without a joint.
The same hinge works with no ถ้า at all. Any topic followed by a comment can take it, which is why ก็ turns up in sentences that have no condition anywhere in them.
- ผมก็ไปpʰǒm ก็ paj
as for me, I'm going too
- ก็ได้ก็ dâːj
fine by me; that'll do
literally 'then, possible'. You will say this several times a day
What not to substitute
French speakers reach for alors and donc and translate those with ดังนั้น or จึง. Both are real and both are heavier: they mark a genuine inference, the kind you would make in an argument.
ก็ marks a joint, not an inference. It is closer to the comma in the French sentence than to any of its words.