Trying to catch up with Gallia after just about grasping Disco Sirius. I am probably missing something obvious but are there any factions trying to be enterprising and set up a Sirius Gallia trade network?
Or is it principally LaBrise and some opaque dealings?
It's still fairly dangerous at the moment. Factions who get clearance permission from the Gallic Royal Navy are probably going to struggle getting in the good books of the Council and the Gallic pirate factions (and vice versa). Therefore, it's a risky operation, no matter which way you approach it.
However, apart from Gallic factions reaching out into Sirius (LaBrise), some notable Sirian factions which have begun trade with Gallia include OSI, Zoner traders, and Mallory & Lambert Logistics, a small independent trading faction. The Council currently has ties to the Colonial Remnant and to the IMG; however, the IMG can only be so friendly with the Council to a limited degree since the Royalists will strong-arm them into submission. The Council has also been a sending a limited number of trade ships on long-distance runs through Sirian House space.
As for other Gallic factions involved in economic dealings with Sirius: GMS have for some time been mining in the Taus and returning the ore back to Gallia.
Edit: This doesn't include the powertraders who take Gold Ore from Dublin into Gallia... but that doesn't count, does it?
In summary, yes, there are more factions doing things, but you might need to delve more deeply to find out exactly what.
Mallory & Lambert Logistics is an inofficial group that connects Sirian and Gallic market. It has dealings with providers of ore that can be sold at Alesia, and exports Gallic products, has a Barge in Orkney for Gallic trading factions so they don't have to enter Gallia... yeah, that's it basically.