A few years ago, my parents, who were married and living separate and apart, set up an SCI subject to income tax. They were the only two partners. My mother has died, and my father has opted for usufruct. As the bare owner of my mother's shares, I...

...became a partner in the company. Do I have to declare the company's profits? 

No. When ownership of shares is divided between a usufructuary and a bare owner, it is up to the usufructuary to declare the sums he or she receives from the company's profits (art. 8 CGI), which will be taxed in his or her name.

Please note: while the usufructuary is taxed on the company's current operating profits, tax doctrine specifies that the bare owner is taxed on exceptional profits (BOI-BIC-CHAMP-70-20-10-20 §100).

Good to know: you and your father can decide on a different distribution. However, this arrangement can only be invoked against the tax authorities if it was agreed in a deed duly registered or included in the company's articles of association, before the end of the financial year (BOI-BIC-CHAMP-70-20-10-20 §100).