Joubert was born in Lawtell in 1931 to Edmond Joubert and Julia Prejean. His father died when Curtis was only six years old, and he began school speaking only French. He graduated from Lawtell High School in 1948.

In 1951, he served in the Korean Conflict. He then attended USL earning his BS degree, then his Masters degree and continued to do some post graduate studies at USL and LSU. In 1988, USL honored Joubert as its Outstanding Graduate from the College of Education. Then in 1999 USL celebrated its Centennial and named Joubert one of its top 60 graduates over the last hundred years.

He is a former teacher, coach, counselor, assistant principal, and former director of the Eunice Vocational Educational Center. In 1980, he was appointed to the State Department of Education in charge of supervising and evaluating Title 1 Programs statewide.

In 1981, Joubert was elected Mayor of Eunice, defeating three opponents including the incumbent. He is only the second man in Eunice to serve at three levels of government – local, parish and state. As one of Eunice’s most popular mayors, Joubert was re-elected Mayor in 1986 and again in 1990 serving for 13 ½ years. Under his leadership, Eunice has gone from just another small town devastated by the oil bust to the capital of the Prairie Cajun Country and a major regional tourist destination.

As mayor of Eunice, Joubert helped organize the citywide Traditional Eunice Mardi Gras Celebration which is now world famous. Today it is the largest rural Mardi Gras celebration in Louisiana. It was Joubert who coined the term Prairie Cajun Capital. When the Republican Convention was held in New Orleans in 1988, the national news media swarmed into Eunice to document the authentic Cajun culture interviewing Joubert and giving all of Acadiana priceless publicity and renewed Cajun pride.

After retiring in 1995, he was then appointed to the La Public Service Commission, which is the regulatory body for Utilities, Transportation and Communications in Louisiana, serving as Executive Assistant.

He was elected to the House of Representatives in 1967 representing St. Landry Parish and is a member of the Board of trustees for Colleges and Universities in Louisiana serving as chairman of Physical Plants Committee and Athletic Committee. As a member of the Board of trustees, Joubert was selected to represent Louisiana at the NCAA policy-making convention in St. Louis, Miami, San Francisco and New Orleans.

He is the founder to the World’s Championship Crawfish Cook-off Contest which is now the largest cook-off in Louisiana. He is the prime mover of the nationally renowned Jean Lafitte Acadiana Culture Center in Eunice sponsored by the National Park Service to perpetuate and interpret the Acadian culture. He is the founder of the weekly and nationally renowned Cajun Music Radio Show held at the Liberty Theatre, being the only show of its kind in the USA.

Under his leadership, Eunice now has its own Depot Museum. Joubert, joined with the LSU-E faculty, was successful in getting a railroad right of way donated to preserve wild flowers and plant life of the original prairie country now know as the Cajun Prairie Wildflower Habitat.

Southern Living magazine featured Joubert in a recent article about “Offices of Excellence” and The TIMES awarded Joubert newsmaker of the Year in 1995. He is a member of the CODOFIL board of Directors.