Hattonchâtel has no train station and no bus service of any practical use for tourists. A car is effectively essential.
By road from Paris, take the A4 motorway east toward Metz and exit at junction 31 (Vigneulles-lès-Hattonchâtel), then follow the D901 and the signs up the hillside. The drive from Paris is about 3 hours and 15 minutes (280 km). From Metz it is 50 kilometres, about 45 minutes. Verdun is 25 kilometres north on the D964.
The nearest train stations are at Commercy (20 km west) on the Paris–Nancy line and at Metz (50 km east). From either you would need to hire a car or take a taxi.