Usually the Roman army on the move, spent a fair amount of time fortifying their encampments. Accordingly, one of the most successful pieces of Roman military equipment, was the shovel. Can't say the later European fortifications were directly based on Roman models (although the locations oft were)...because Gaullic fortified towns already existed. However the Carolingians did copy the fortified Roman Gate for their own useage...and then stuck it on churches.
As far as Roman individual fighting tactics, as already mentioned, a good place to look is in Roman reliefs, many of the mosiacs dealt with gladiatoral conflict.
Although some periods tended to go back to Rome as a model (ie Carolingians and Italian Renn) they kept thier own tactics, styles and weapons for individual conflict. I.E. The Italians, copied some of the martial 'look' of Rome, but only in the clothing.
Well outside of the period of this forum, but the Napoleonic military copied the gladius for some units, as did the US in the civil war...but these were really symbols rather than useable weapons.


