What is the ruling on brokering a commercial franchise deal that includes mixed (gender) training in a foreign country, mixed (gender) future work, and usurious banking transactions, knowing that mixing (of genders) and usurious transactions are widespread?

Brokerage is permissible in principle. Doubt about the occurrence of something unlawful in transactions does not necessitate prohibiting assistance with them, because selling something that could be used for unlawful purposes to someone whose use of it is doubtful is not forbidden. And even if there is knowledge of mixing [of funds] that is not the intended purpose of the transaction, the assistance is not direct, so it is not forbidden.

The summary of what the Assembly of Islamic Jurists concluded is that assistance in sin and transgression falls into four categories: direct and intentional, direct and unintentional, intentional but indirect, and neither direct nor intentional. The first three types are forbidden, while the fourth type is permissible.

Doubt about whether the funds of a transaction are unlawful does not necessitate prohibiting assistance with it, as the basic principle for things is permissibility and lawfulness. There is no obligation to investigate the money of contracting parties. Permissible dealings with usurious banks, when there is a need and widespread affliction (common plight), are not forbidden.