Complex sentence: The French advanced cautiously, as part of the main offensive by the First and Second armies into Lorraine and reached the area west of Mulhouse by 16 August and then fought their way into the city by 19 August.
Split into simpler sentences: The French advanced cautiously, as part of the main offensive by the First and Second armies into the province of Lorraine, and reached the area west of Mulhouse by 16 August. They then fought their way into the city by 19 August.