At the federal level Canada has two official languages, but in most cases BC courts only accept court filings in English. Criminal matters are the exception, allowing either official language per s.530 of the Criminal Code. This is because the official language policy of Canada largely applies to federal services and does not infringe upon each province’s right to decide its own language use.
When Canada was first formed, British Columbia exempted itself from s.133 of the Constitution Act, which dictated that either French or English could be used for debate in the House of Parliament. This means that MPs from British Columbia cannot be required to use French when debating in Parliament or drafting statutes. It also means that BC has no officially mandated language, either French or English, but English is used as a de facto official language despite there being no legislation specifically granting it that standing.
Since the province recognizes no official language, it allows the courts to set their own rules concerning use of language in court documents. Rules 21-1(2) and 22-3(2) of the Supreme Court Family and Civil Rules respectively, set out that all documents prepared for use in court must be in the English language, unless the nature of the document renders it impractical. That means that any documents in a language other than English must be translated before the court will accept them.
The use of French filings in BC courts was challenged in the mid 1980’s. In McDonnell v. Federation des Franco-Colombiens (B.C.C.A.)  B.C.J. No. 730 the BC Court of Appeal held that the British Columbia Supreme Court rule stating that court filings must be made in English did not violate the Canadian Charter of Rights and Freedoms and that sections 16-22 of the Charter did not apply to British Columbia since the province does not recognize an official language.
The ability to file documents in French was again challenged in 2013 in the Canadian Court of Appeal in Conseil scolaire francophone de la Colombie‑Britannique v. British Columbia  2 S.C.R. 774 , where it was upheld that BC was allowed to limit the filing of court documents in provincial and supreme courts to English only.
Unlike the Supreme Court, BC Provincial Court (Family and Small Claims) has no rule specifically dictating the use of English in court filings, though they do have rules commanding the use of their approved forms, which are in English.