This study will include participants with various types of cancer known as soft-tissue sarcomas. Tissues that can be affected by soft tissue sarcomas include fat, muscle, blood vessels, deep skin tissues, tendons and ligaments. Soft tissue cancers are rare and can occur almost anywhere in the body. Part 1 of this trial will study the safety and the level that adverse effects of the study drug tazemetostat in combination with doxorubicin (current front line treatment) can be tolerated (known as tolerability). It is also designed to establish a recommended study drug dosage for the next part of the study. Part 2 will evaluate and compare how long participants live without their disease getting worse when receiving the study drug plus doxorubicin versus doxorubicin plus placebo (dummy treatment).