The son of Louis Béïque and Élisabeth L'Homme dit Artois, Frédéric-Liguori Béïque was born in Saint-Mathias-de-Rouville on May 20, 1845. In 1875, he married Caroline-Angélique Dessaules, the only daughter of Louis-Antoine Dessaules, seigneur of Saint-Hyacinthe and nephew of Louis-Joseph Papineau.
After studying law at Université Laval, he was called to the Bar in 1868 and went on to become Honoré Mercier's counsel at the inquiry commission on the Baie-des-Chaleurs railway. But he made his fortune in the banking business. He is a co-founder of Banque d’Hochelaga.
In 1902, he was appointed senator by Canada's Prime Minister Wilfrid Laurier, who entrusted him, the following year, with writing the Bank Act. Associated with Canadian financial interests, he was the founder of the General Trust of Canada in 1909 and a member of the Board of Directors of what was then called the Canadian National Bank, from 1928 until he died in 1933.
In 1909, he bought Orchard and Doran farms from the municipality of the Parish of Lachine (present-day LaSalle). These farms were located near the entrance to the Montréal Aqueduct and became the Béïque estate, covering an area equivalent to the Town of Hampstead. It wasn't until the 1960s that a housing complex was built there.