Commentary
Charles Cawley sats that "The primary source which confirms his parentage has not yet been identified.", but then assigned him as the son of Gerhard (killed 910) who his lists as a possible son of Adalhard IV, who died in 890.

Stewart Baldwin: 'The main evidence for the parentage of Godefroid is indirect, coming from the relationship of two individuals in a famous case regarding consanguinity, that of Otto of Hammerstein and his wife Irmingard/Ermengarde ["Gebehard et Udo nepotes, filii duorum fratrum. Gebehard genuit Cunonem. Udo genuit Ottonem. Cuno genuit Cunonem. Heribertus genuit Ottonem. Item ex alia parte: Godefridus et Gerbirhc nepos et neptis. Godefridus genuit Irmingardam. Gerbirhc genuit Imizam. Imiza genuit Ottonem." MGH Const. 1: 639]. Here, the first part mentions paternal relatives of Otto who do not concern us here, and "nepos et neptis" is to be interpreted that the Godefroid and Gerberga of the record had a common grandparent, i.e., that they were first cousins. ... [chart omitted] ... How this information is used depends on the identifications of the individuals involved. The key observation was made by Schenk zu Schweinsberg, who noted that the name Imiza was a hypochoristic form (roughly, "nickname") of Irmintrud/Ermentrude, and that the Gerberga and Imiza in the consaguinity notice of Otto and his wife should be identified with the Gerberga and Ermentrude of the Vita Adelheidis. He also identified the Godefroid of the notice with Godefroid, count of Verdun [Schenk zu Schweinsberg (1904)]. Both of these identifications are now widely accepted [See Hlawitschka (1969), chapter II, for the most detailed discussion]. Accepting this evidence that count Godefroid of Verdun was a first cousin of Gerberga, daughter of the present Godefroid, we are still left with several possibilities. If we accept also that Godefroid's wife Ermentrude was the mother of Gerberga (an assumption made stronger by onomastics), then we have that one of Gozlin and Uda (parents of Godefroid of Verdun) was a sibling (or half-sibling) of one of the older Godefroid and Ermentrude (parents of Gerberga). Given that there are four possibilities here, it is not surprising that different interpretations of this evidence have appeared. ' He then goes on to several possibilities.
Family
ClaimDetailEvidence
SpouseErmentrude (e891-) 
Child +Gerberge (e923-) [S978] [S1414]
research
Attributes
ClaimDetailEvidence
GenderMale
NameGodefroid , Count Palatine [S1415]
research
NameGottfried , Count Palatine [S1415]
research
NameGottfried , Graf [Matfriede] [S978]
research
Timeline
ClaimDateDetailAgeEvidence
Birthest 891
 
Sources
IndexTitle
[S978] Cawley, Charles, "Foundation of Medieval Genealogy (Medieval Lands - Franconia Nobility)" (2006-7 (v1.1 Updated 02 January 2007)) (https://fmg.ac/Projects/MedLands/FRANCONIA.htm).
[S1415] Baldwin, Stewart, "The Henry Project - Godefroid" (April 5, 2007) (https://fasg.org/projects/henryproject/data/godef001.htm).