Da Costa, 24, had a goal and an assist in nine games for the Senators last season.
He spent the majority of last season in the American Hockey League with the Binghamton Senators, leading the team with 25 assists and tying for the lead with 38 points.
In 35 NHL games, Da Costa has four goals and seven points.
Da Costa was signed by the Senators as an undrafted college free agent on March 31, 2011, after two NCAA seasons with Merrimack College in Hockey East. In 67 collegiate games with the Warriors, he had 30 goals, 90 points and 83 penalty minutes.
Da Costa is the only French-born player to be signed by the Senators. He has represented France four times at the IIHF Ice Hockey World Championship.