It really looks like a Fiat. My Father used to own Fiat cars, and the front round big headlamps, metal mask, the tailights, long and tall,big spacy glass with small frames and the cut of the car is very Italian. Easy to be confused with a Fiat. Fiat 850, Fiat Brava, etc.
Also the tires help, Fiats used to come from factory with well shaped wheel /tires, always that sporty look, most other cars need aftermarket wheels to achieve that look. Many Fiats would come from factory with wheel/tires looking like your 1000 wagon.
Jaime.___________________________