Before the interview, with the fee paid and the equipment bought, so the funds are at risk on the day. Negotiate an opening date with the franchisor that allows for visa processing, and do not start operating from the United States before issuance.
Commit first, open after issuance
Franchisors usually want a signed agreement, the fee and a training date. The E-2 application needs the fee paid and the equipment purchased before the interview, because uncommitted money is not an investment. Sign, pay and buy, then apply.
The gap between payment and visa issuance is the buyer's exposure, and the franchise agreement should address it: an opening deadline long enough to cover consular processing at the relevant post and a clause allowing rescheduling of training if the visa is delayed. Franchisor training inside the United States before issuance may be acceptable as a visitor if it is classroom instruction with no productive work, but running service calls is not; confirm the training's content in writing first. Resolve the state licence question in parallel, since examination dates can take months.
Once issued, E-2 is renewable while the business continues to qualify, so the first opening date matters less than opening lawfully.