• https://fmg.ac/Projects/MedLands/burgkgenev.htm#GeneveMMathildeBurg...

i) GERAUD ([1010/20]-after [1065/80]). .. ... ...

[m firstly GISELA, daughter of ---. Guichenon names Gisela as the first wife of Géraud Comte de Genève[26]. The primary source which confirms her marriage has not yet been identified.] [A family relationship is indicated between Rudolf von Rheinfelden King of Germany and Géraud Comte de Genève: a continuation of the Annales of St Gallen records that in 1064 “Rudolfus dux” attacked “Burgundiones” and expelled “sui sororini...rebellis Geroldi” from Geneva[27]. The term “sororinus” is rarely encountered in medieval documents. Ducange provides three possible definitions: “sororis maritus”, “uxoris frater”, and “filiolus sororis”[28]. The second of these can be excluded in the context of the Rheinfelden family given our knowledge about the families of Rudolf’s wives, as well as the third given the chronology of the lives of Géraud and Rudolf which suggests that the former was born earlier than the latter. “Sister’s husband” is therefore the most likely possibility, with which Hlawitschka agrees[29]:
if that is correct, Géraud married --- von Rheinfelden, daughter of Kuno Graf von Rheinfelden & his wife ---. This is consistent with “sororinus” being derived from “soror” and maybe being a variation of “sororius”. As shown here, Géraud is recorded with two possible wives. Given the likely dating of his [second] marriage, it is difficult to assess whether, in this scenario, his [first wife] Gisela or his [second] wife Tetberga would have been the daughter of Kuno Graf von Rheinfelden. It should be noted that Armin Wolf, linking the etymology of “sororinus” with “sobrinus” and by extension “consobrinus”, suggests that Géraud and Rudolf were first cousins, sons of two sisters[30]. However, this interpretation requires reading “sororini” as “consororini”, which stretches the natural interpretation of the passage. If Géraud’s wife was Rudolf’s sister, presumably she could have been the same person as Kuno’s daughter shown in the document SWABIA NOBILITY (in which case she would be identified as Géraud’s [first wife] Gisela).]

m [secondly] ([1060/70]) as her second husband, TETBERGA, widow of LOUIS Seigneur de Faucigny, .. ...

There has been unsubstantiated speculation that she was married to: Charles Constantine of Vienne

Charles Constantine, Count of Vienne

From Wikipedia, the free encyclopedia

He was married to Thiberge de Troyes. Their daughter Constance of Vienne was wife to Boso II of Provence and ancestor of the Counts of Provence.

~~~~~~~~~~~~~~~~~

Theutberge

has been linked on Geni  as  Daughter of Amadeus Count of Savoy, Amadeo, I, Thiburge de Arles, Garnier de Sens, Werner ou Vernaire, Garnier de Loches, Adelaide d'Albon and Teutberge or Thiberge Count of Sens & Troyes (of Provence, d'Arles) however as I can find no such connection I have detached these parents making this record in case a source is found to support any of them.

===From Medlands:===

http://fmg.ac/Projects/MedLands/BURGUNDY%20Kingdom.htm#GuillaumeFau...

LOUIS . His parentage is confirmed by the charter dated 4 Sep 1119 by which his son "Wido…Gebennensis episcopus" donated "ecclesiam de Condominio" for the souls of "patris mei Ludovici et avi mei Ermenradi…" to Cluny[957]. Seigneur de Faucigny. [1030]/[1060]. m as her first husband, TETBERGA, daughter of ---. Her marriage is confirmed by the charter dated 4 Sep 1119 by which "Wido…Gebennensis episcopus" donated "ecclesiam de Condominio" for the souls of "…matrie mee Teberge" to Cluny[958].

'''She married secondly [as his second wife,] Géraud Comte de Genève'''

Her second marriage is confirmed by the undated charter under which "Aymo comes Gebennensis et filius meus Giroldus" founded the priory of Chamonix, signed by "uterini fratres comitis, Willelmus Fulciniacus et Amedeus…"[959]. Louis & his wife had three children:
Guillaume, Guy & Amedee Géraud Comte de Genève & Theutberge had one child: AIMON [I] ([1065/80]-12 May [1125/28]). "Patris Geraldi et fratris Cononis, comes Aymo successor" donated property to the church of Leman, at the request of "fratris Burchardi monachi", by undated charter[728]. Comte de Genève

There is speculation that Geraud and his second wife first had CONON (-before 1080). "Cono Geraldi comitis filius" donated property to the abbey of Ainay, with the consent of "Geraldi comitis patris sui", by charter dated to [1061][727]. The chronology suggests that Conon must have been considerably older than his brother Aimon [I] and therefore was probably born from his father´s [first] marriage

Count Gerold of Geneva - was born about 1012, lived in Geneva, Switzerland and died about 1045 . He was the son of Count Simon I of Gevena and Countess Bertha of Flanders.

Count Gerold married Countess Gisela of Geneva. Countess Gisela was born about 1020, lived in Switzerland.

 Then Count Gerold married Thietburge. Thietburge was born about 1025, lived in Geneva, Geneva, Switzerland.

Children with Countess Gisela of Geneva (Quick Family Chart)

i. Joan de Geneva was born about 1040, lived in Geneva, Switzerland.

Joan married Count Amadeo II of Savoy. Count Amadeo was born about 1032, lived in Geneva, Switzerland. He was the son of Eudes Savoy and Adelais Suza. He died on 26 Jan 1080 .

• https://genealogics.org/getperson.php?personID=I00027361&tree=LEO {no surname}