ESTA form and first names

Update 02 Oct 2018

The ESTA site has now changed its help text. It now states:

In the First (Given) Name field, enter ALL first (given) names exactly as they appear on your passport in the first (given) name field. The first (given) names are required to complete the application. If you have no first name, then enter the letters FNU which stands for First Name Unknown.

(emphasis mine).

Note that you can now upload your passport photo and have the MRZ read directly, which should fill all relevant data for you.

As an aside, I just noticed that by current french passport lists all my given names in the MRZ, while my previous passport only listed the first one.

--- original answer ---

Yes, that's right.

In the United States, given names are usually split as first and middle names.

The first name only includes a single name, while you would put any additional given names as middle name (they're used to a single middle name, but you can add more).

The ESTA form specifically asks only for the "First (Given) name", and the associated help bubble states:

Do not include the middle name in this field

Also, as it is quite common for French people to have multiple given names, I checked the French version of the ESTA site. That one says:

Dans le champ Prénom, tapez votre premier prénom. [...] N'incluez pas le deuxième prénom dans ce champ.

Which can be translated as:

In the First (Given) name field, type your first given name. [...]. Do not include the second given name in this field.

tl;dr: Officially you should use them all, but maybe both ways are fine?

I think you were wrong and should have filled the ESTA form with your 3 first names. In reality, it looks like people are reporting here and there having no problem with either way.

Officially though, it looks like the ESTA application form provided by the U.S Customs and Border Protection recommends to put the entire "First name" field as shown on your passport.

Taken from the help text displayed when I hover over the question mark icon next to the First (Given) Name field:

In the First (Given) Name field, enter ALL first (given) names exactly as they appear on your passport in the first (given) name field. The first (given) names are required to complete the application. If you have no first name, then enter the letters FNU which stands for First Name Unknown.

(Emphasis mine.)

My French passport says "First Name: David,Eric,Jacques", so that's what I'll put in my application. If my passport had a middle-name section, I would ignore it.

Update: it is also possible to use a passport scanning feature by uploading a scan of your passport. This feature worked quite well, and filled the First (Given) Name form input field with my three first names, separated by a space, in capital letters: DAVID ERIC JACQUES.

No, that's not right. You have to give your name as in the passport, including all first names.