[girigiri]

交感…? You might have wanted to say 同感?

あっ。。。　それは自分に覚えてできなかったちゃんと 言葉です。ありがとうございました。ちなみに、ゆりと ころさんが覚なんですか？

I went to Café Du Monde and ate beignets in Ikebukuro, Tokyo

beignets? あっ。。。あたらしいことばですじぶんに。おいしそう みたい。"beignets in Ikeburo" ー　何らかのソースなんで、ことによったらフリッター ですか？
I went to (the) Café Du Monde in Ikebukuro, Tokyo and ate beignets. ○
または
I had beignets at (the) Café Du Monde in Ikebukuro, Tokyo.　◎

I’ve been to the original Café Du Monde Coffee Stand in the New Orleans French Market in the US. I had a good time and enjoyed their delicious beignets.

I've →　I have
"... in the US. I..." → "... in the US, where ..."

This should be the opening sentence. You are using the American Cafe du Monde as the base point for comparison. Because you are referring to two different Cafe du Mondes, it is necessary to use the definite article "the" for each.

The beignets are served in an order of three big ones in the US, and six small ones in Japan.

Disordered sentence, but can be understood without difficulty.
"A serve of beignets in the US has three large ones, while/where a serve in Japan has six small ones." (better, but still not pretty.)
"Three large beignets make up a serve in the US; where/while in Japan, there are six small ones." Rather than have this, it may be better to merge these descriptions with the relevant earlier sentences, .

The differences may be for three reasons.

The servings ( 1. the US serving, 2. the Japanese serving.) are the point of comparison here - therefore, "three reasons for the difference."
Emphasise: this is speculation - eliminate the risk that someone might think you are claiming to have investigated the reasons behind the difference.

"Three possible reasons for the difference come to mind."

The first reason would be that three large beignets are too much for a Japanese woman.
The second would be that Japanese women hate getting their hands greasy.
The last reason would be that Japanese women hate the flying powdered sugar.

First, second, third ... acknowledge that there may be other reasons.

Do you think big ones would be better? I prefer small ones!

I prefer small beignets, which do you prefer?

(Having read all of the passage now, these things sound like poffertjes. If so, small is definitely better.)

@Koir: ??? How do you eat your pancakes?