Bizimungu was convicted for embezzlement, inciting racial animosity and criminal association.
"We are demanding a full acquittal," said the lawyer, Jean-Bosco Kazungu on Thursday.
"We are not happy with the judgement and the sentence," he said, adding "You can not simply sit and just wait for 15 years to end."
Bizimungu and seven co-accused were convicted and sentenced on Monday.
The former president was found guilty on three charges: diverting public funds, spreading rumours liable to incite civil disobedience and criminal association, each of which carried a five-year jail term.
Symbol of reconciliation
A Hutu, Bizimungu held office from 1994, when the Tutsi rebel group that had just seized power installed him as a symbol of reconciliation in the wake of the slaughter of some 800,000, mostly Tutsi Rwandans. Bizimungu was hounded out of office in 2000.
The criminal association accusation, and a dropped charge of threatening state security for which prosecutors hoped for a life term, are rooted in his creation of a political party in 2002, PDR-Ubuyanja, which was immediately declared illegal.
"We are not happy with the judgement and the sentence"
Bizimungu has been detained since that year.
The incitement to civil disobedience charge covers the more specific accusation that Bizimungu, a member of the country's Hutu majority, was encouraging hostility towards the small Tutsi minority.
Human rights group Amnesty International has criticised the trial saying conditions of the arrests and detention, and the trial itself, fell far short of international standards of fairness.