ESTA did not exist in those days, but the visa waiver program (VWP) did. Most likely, you and your parents traveled under the VWP. The practical consequence of this is that you will have filled out green I-94W forms instead of white I-94 forms just before arriving in the US (in addition to the blue-and-white customs form that is still in use today). Therefore:
As a French child, did I need a visa to get in the US in 2004 and 2006?
No, you did not need a visa.
Credit:stackoverflow.com‘
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