You are fine to reenter using your US passport, and this does not affect any of your rights under EUSS. If you are concerned that entering with a different passport than your EU one means you are not entering with EUSS status, that is not the case. Your EUSS status applies to you, not your passport. When you apply for settled status (or when it is automatically upgraded) the Home Office use things like tax records to confirm UK residency, not (solely) the entry/exit records for your passports, since these are often incomplete.

Using an American passport you would be fine to enter using the ePassport gates. You may wish to register your French ID card to your UKVI account to make sure it is linked to your EUSS status in case you do need to speak to a border officer.

Note that this will make the ID card the primary document, and the one you use to log in to your UKVI account. Once you have your new French passport you should then add that document too.

You are fine to reenter using your US passport, and this does not affect any of your rights under EUSS. If you are concerned that entering with a different passport than your EU one means you are not entering with EUSS status, that is not the case. Your EUSS status applies to you, not your passport. When you apply for settled status (or when it is automatically upgraded) the Home Office use things like tax records to confirm UK residency, not (solely) the entry/exit records for your passports, since these are often incomplete.

Using an American passport you would be fine to enter using the ePassport gates, unless your daughter is too young to use them. You may wish to register your French ID card to your UKVI account to make sure it is linked to your EUSS status in case you do need to speak to a border officer.

Note that this will make the ID card the primary document, and the one you use to log in to your UKVI account. Once you have your new French passport you should then add that document too.