As was noted on the beta forums, all enemies have uniform elemental resistance. Here is the description of Bard's skill Foe Requiem:

Reduces all enemy elemental resistance by 10%. MP is drained while singing. Effect is lost if targets move out of hearing distance, and ends upon reuse. Cannot be used with other songs.

Here's the description of the Archer skill that I tested this with, Windbite:

Deals wind damage with a potency of 60. Additional Effect: Wind damage over time. Potency: 45 Duration: 18s

For all of the following damage numbers, all conditions were the same regarding gear, level and durability of the Bard (lvl 41).

Here's a sample of streams of auto attacks against a lvl 1 Striking dummy in Whitebrim Front (critical attacks omitted):
75, 76, 76, 70, 76, 72, 70, 75, 72, 70, 73, 69, 76, 75
Here's a sample of streams of auto attacks against a lvl 1 Striking dummy in Whitebrim Front (critical attacks omitted) in addition to Foe Requiem active:
72, 71, 71, 72, 75, 73, 72, 71, 70, 69, 74, 73, 75, 69

From this sample (and the skill description) it can be inferred that as intended, there is no drop in damage by using Foe Requiem (unlike the other songs). In addition, there is no increase of damage (as intended) by non elemental attacks.

Next here is a sample of a stream of Windbite (just the attack) against a lvl 1 Striking dummy in Whitebrim Front (critical attacks omitted):
45, 46, 46, 45, 48, 44, 46, 46, 48, 48, 44, 43, 45, 48, 48

Here is a sample of a stream of Windbite (just the attack) against a lvl 1 Striking dummy in Whitebrim Front (critical attack omitted) in addition to Foe Requiem active:
44, 45, 48, 47, 44, 47, 48, 44, 48, 47, 46, 47, 47, 44, 47

Since in the description of Windbite, the Damage over Time is also "wind damage" dealt, I will include these numbers as well.

Here is a sample of a stream of the Damage over Time of Windbite against a lvl 1 Striking dummy in Whitebrim Front (critical damage omitted):
37, 37, 36, 37, 36, 37, 36, 37, 35, 34, 34, 36, 35, 36, 35, 37

Here is a sample of a stream of the Damage over Time of Windbite against a lvl 1 Striking dummy in Whitebrim Front (critical damage omitted) in addition to Foe Requiem active:
37, 36, 36, 35, 35, 34, 36, 35, 37, 34, 36, 34, 36, 37, 34, 36

As can be shown by the data sets the average damage (nor the ranges of damage for that matter) had not changed in any way. This leads to the conclusion that Foe Requiem is not working as intended and may actually be doing nothing (except draining MP). In another scenario, It may be the case that Windbite is not dealing wind damage as it should. In either case, there is a bug with one of the archer/bard skills and this needs to be investigated.