A Franco-Ontarian, he was elected as councillor for Cumberland Township in 1976, and remained a council member until his election to the Legislative Assembly of Ontario in the 1981 provincial election. Boudria defeated Progressive Conservative incumbent Joseph Albert Bélanger by 5,172 votes in Prescott and Russell, and served in the legislature for three years as a member the Ontario Liberal Party, which was then the official opposition to the Progressive Conservative government, led by William Davis.

He left provincial politics to run for the House of Commons in the 1984 federal election. Boudria won a convincing victory in Ontario's easternmost riding, Glengarry—Prescott—Russell, even as his party suffered a landslide defeat against Brian Mulroney's Progressive Conservatives. Joining the opposition benches of the Commons in 1984, he became a member of the Liberal Rat Pack with Brian Tobin, Sheila Copps and John Nunziata.

Boudria served in several positions in Jean Chretien's cabinet, and as a Chretien loyalist, he did not run again in 2006.