Everyone I know from over there seems to call it eggy bread. Particularly the older folks. French toast seems to have more currency now. Particularly with younger folks, and anytime its cooked in the fairly standard now way with milk or cream and flavorings.
Also the description of just beaten egg isn’t neccisarily the way its usually made there or anywhere at the moment, but supposedly the traditional recipe in the British isles. As in if you look at old recipe books or even historic recipes. My grandfather leaned to make it that way growing up in the 20’s and 30’s in Ireland.
Larger point being we apparently call it french toast (wherever we call it french toast) because the particular recipe used, with sugar, milk and flavorings. Is apparently French and/or introduced to the US and British isles via France.