You are mentioning about equity split. From your query, it is not clear whether a foreigner is investing in India with you. Or you are investing in a foreign country with a foreign colloborator.
If it is investing in India, the same is governed under FEMA Rules under Foreign Direct Investment.
If it is investing abroad, the same is governed under FEMA Rules under Overseas Direct Investment or if invested as an individual under Liberalised Remittance Scheme rules.
In both scenarios, you need to comply with the RBI rules which include submission of papers/documents online through your bank.
For the above, you need to consult a Chartered Accountant.
As to entering into an agreement you can do so through a Lawyer specializing in international agreements clearly defining roles of each person and jurisdiction also in case of a dispute. The agreements are subject to FEMA regulations which need to be examined before proceeding further.