Filmjölk is a traditional fermented milk product from Sweden, and a common dairy product within the Nordic countries. [Wikipedia] In one sense, Filmjölk is to Sweden as Yogurt is to Bulgaria. The basic version does not contain any Lactobacillus. I have included the hierarchy below to better understand where things are at.
What is in it?
- Lactococcus lactis
- Leuconostoc mesenteroides (also found in true Kimchi and many traditional fermented food)
There are a variety of commercial versions with additional bacteria added, for example, Lactobacillus plantarum 299v has been added to one commercial variety.
From uBiome samples shared… I looked at the Families these later two are in.
- Only one patient had any Leuconostocaceae and the level was less than 2% of the normal value.
- Only one patient had high Streptococcaceae, most had less than 10% of the normal value.
In terms of encouraging biodiversity, it seems like a desirable item. Unfortunately, CFS has too many Firmicutes over all (post) which means we are in a balancing act.
I was unable to find any meaningful studies of Lactococcus lactis in isolation. There were multiple studies of it in combination with other bacteria showing changes of brain activity (i.e. improved mood, less depression).
What is the next test? Histamine production
Histamines severely impacts a subset of CFS patients.
- Leuconostoc mesenteroides – significant producer 
- Lactococcus lactis – “nisin-producing Lactococcus lactis appears to inhibit histamine productions  and has no impact on histamine by itself (see post)
This leaves the histamine content fuzzy — unfortunately.
What is the next test? D-Lactic Acid production
D-Lactic acidosis is common with CFS.
- Leuconostoc mesenteroides – significant producer  
- Lactococcus lactis – significant producer 
Based on the data available, the weight of various factors says it should not be taken. We should also note that Kimchi is very similar, and should also be avoided.