If there is a dedicated tool for this, I have not heard of it.
FPC ribbons usually have a "stiffener" in the form of a tab on either end. This adds some stiffness to keep the end from bending too much. And for the final push/seating, you can grab the ribbon behind this neck so there's a ridge to push against.
I don't know if this is feasible to do with your project, but all FPC manufacturers can add extra things like this for an added cost. You've probably already spec'ed the connector and have matched the board thickness, so this is not likely a realistic option. Plus, your connector might be double-sided. Even in these cases, you might consider adding a strip of stiffener just a bit outside of where the connector ends, just to give that ridge to push against. Maybe a 0.2mm polyamide stiffener.