I found something similar when I went from drop bars, on my Motobecane Grand Jubilee, to Mustache bars, fitted with Barcons. The front end felt unusually light and almost unstable. I did get used to the difference but I am wondering if stem length might have something to do with it?

This is the stem, original to the handlebars. The stem reach is 65mm, as I recall...


And this is the stem holding the same bars as fitted to my Motobecane...