Alan has given a pretty clear description. I do have an older rig than you but on my Maramu the tack of the foc d'artimon also goes to the U bolt on the deck in front of the dodger, the halyard is on the port side of the mizzen and the sail sheets in via blocks on the aft quarter. Obviously only for off the wind sailing when you won't need to change tack as it gets in the way of the boom.
The trinquette, in my understanding, can be a staysail or a smaller hank-on genoa, suitable for strong winds. On Popeye the trinquette is the latter and hanks on to the solent stay. The tack goes to the deck fitting with a short wire or strop to keep the foot of the sail above the guardrails, the halyard comes down on the port side of the mast, and the sail sheets in using the genoa sheet blocks. If you aren't sure what a solent stay is, it's an additional removable wire stay that is just inside the forestay and attached to the mast just under the forestay. It doesn't need extra running backstay support as it attaches so close to the top of the mast. Most of the time the bottom end attaches to the toerail near the shrouds with a pelican hook and it has a special heavy duty windable fitting to give it tension when connected up for use.
My trinquette also has one set of reefing points like a slab reefing mainsail and is heavy cloth so it can be used with a smaller area. It is useful in winds above 30kts or prolonged beating where a roller reefed genoa would have a baggy shape. I have just recently been using it whilst the genoa was having the UV strip repaired and have used it before when there was a problem with the roller furler. A solent stay also gives peace of mind that there is a backup if the forestay has a problem. I have always assumed it was factory fitted when the boat was new.
John, Maramu #91, Popeye