I took some time to look at the differences in a real and fake Lacoste and some ways to tell if they are fake. I bought one from Holt Renfrew and one that I knew was fake off eBay. But if you are just looking around, and you see someone wearing Lacoste, this is how to tell if it is fake.

FAKE
-The buttons should never say Lacoste on them
-Crocodile stitched on the right breast of the shirt.
-Button should not have the crocodile on it.

REAL
-If the tag says "Designed in France, Made in Peru"
-On the inner tag, if it says Devanlay on the inside,
-Size will be a number, not a letter. (Ex. Size 4, not S)

TIPS
-Avoid shirts made in Asian countries.

I will compare two shirts, the blue one is real and the white one is fake.

Crocodile

If you look at the blue shirts croc, it is a lighter green than the dark green on the white shirt. Also, the tongue of the croc on the blue one is longer and more detailed than the white.

Comparison between Crocodiles

Buttons
The button on the white shirt says LACOSTE on it and the blue one doesn't. Also the blue one is made out of pearl while the white button is made out of plastic.

Comparison between Buttons

 Tags
The tag on the blue shirt says Designed in France Made in Peru, the white one does not even have a tag to say that. All it has is one tag that says Lacoste with a fake croc on it. The blue one has 2 tags.
 
Comparison between Tags

 Wash Tags
This is blatantly obvious, the tags look completely different. These are the tags that are on the inside of the shirt that say how to wash and the material the shirt is made out of. It is real if somewhere on the wash tag it says Devanlay. The blue one does, the white one does not.

Hope this helps! Don't be caught wearing a fake!