This is a good question and caused me to search errata, rules book, and dig out the "Friend?" card itself, along with others. The rules and errata say nothing, from what I saw, about when and if a Keeper chooses the actions for an investigator (though I did skim the rules book admittedly, so kudos to those who do find it). Because the game is competitive, I doubt final say will be the Keeper's.
The "Friend?" card states, "The Keeper may move you up to 1 space and then choose an investigator for you to attack as if he were a humanoid monster. The keeper chooses which of your weapons to use. Then discard this card."
The first sentence and last sentences are clear, the latter meaning the card will be discarded and you will have no lingering mental trauma, and the former stating that the Keeper may move your character up to 1 space (his choice) and then he chooses an investigator for you to attack as if he [or she] were a humanoid monster (his choice).
The problem lies in the middle sentence: "The keeper chooses which of your weapons to use." Whether it was intended or not that the Keeper makes choices on the card, the quote states the Keeper is merely choosing the weapon to be used, and in the former sentence that he, the Keeper, chooses for you an investigator to attack. The card states nowhere the Keeper has the ability to make card choices; that is for the investigator player him or her self to decide, as the card, again, states, "he (the Keeper) chooses an investigator for YOU to attack." The Keeper also is choosing the weapon of choice, which must be used to attack with, but from then on the investigator makes all valid choices because of "Friend?"'s wording. "Friend?" is not a card that lets the Keeper completely take over the investigator's turn, only add to it.
I believe Shotgun will alleviate as an example what should happen in just about every case, so let's take a look.
The map set-up is The Fall of House Lynch, and Joe Diamond is in the mid-section of the Foyer with Jenny Barnes on the second floor Foyer space that is adjacent to the Basement Stairs. Joe has 0 sanity. A maniac appears from the Dining Room and Joe fails his sanity check; the Keeper then plays "Friend?" on Joe. "Friend?" gives the Keeper the option of moving Joe one space. The Keeper chooses to move Joe into Jenny's space. The Keeper then chooses Joe to make an attack on Jenny and to use the Shotgun. A humanoid monster card is drawn for Joe to attack with. He must test Willpower for his ranged attack, and he passes. Jenny takes 6 damage. She takes 4 from the shotgun regularly, and then 2 additional damage because the Shotgun says, "Deal +2 damage when attacking a monster in your space." Because Jenny is treated as if she were a humanoid monster this action, she must take the additional 2 damage. "Friend?" is discarded. Then, if still alive, Jenny makes her sanity roll for the maniac.
Now lets restart the example and say Jenny is one more movement away, and that she is on the Basement Stairs instead. The Keeper uses "Friend?" to again move Joe to the space Jenny had previously occupied in the former example. Joe is now adjacent to Jenny though, and the Shotgun says, "Action: Attack a monster within 1 range (you may attack through a door)." Though Jenny would be a valid target with the Shotgun's ability, "Friend?" only allows the Keeper to choose a single space to move into (if he wishes), a valid target, and a weapon for the investigator to fire with. Jenny is a valid target because the weapon that would be chosen is the Shotgun, which has the ability to shoot through doors (which one does separate Joe and Jenny). However, Joe is the attacker, not the Keeper, and the Keeper has no ability to make choices on Joe's card, just which weapon Joe must use. Joe chooses not to attack through the door, fizzling the attack because the target is no longer valid. "Friend?" is discarded.
To clarify the topic's title, "Friend?" would force the wielder of the Tommy-Gun to make an attack, but the investigator him or her self would choose whether or not they wanted to attack a second time. Whether or not FFG had intended this, they should have designed the "Friend?" trauma card to say something to the effect of "...The keeper chooses which of your weapons to use. When a weapon ability says the investigator may choose a specific action, the Keeper chooses instead. Then discard this card."
Otherwise, good post and I would encourage you to email this to FFG because I am sure they would like a clear and concise clarification for "Friend?" in an updated errata in the future.