From the Foundation for Medieval Genealogy page on France Capetian Kings:

The name of Robert's first wife is not known. However, as King Robert's known wife Béatrix de Vermandois could not have been the mother of his daughter Adela (married to the brother of Béatrix) it is assumed that this earlier marriage is correct.

According to Europäische Stammtafeln[63], Robert's first wife was named AELIS. This may be based on the 21 May 907 donation of Rebais abbey to the church of Paris which refers to "comitis Rotberti et Adele comitisse"[64]. However, as shown below, this is more likely to refer to Robert and his daughter than his wife.

Robert married secondly ([897]%29 BEATRIX de Vermandois, daughter of HERIBERT I Comte de Vermandois & his wife --- ([880/83]-after 26 Mar 931).

The Historia Francorum Senonensis records that "sororem Herberti" was the wife of "Robertus princeps" who rebelled against Charles III "le Simple" King of France[65]. Guillaume de Jumièges records that Duke Robert's wife was the sister of Héribert, by whom he had a son Hugues[66]. "Hugo rector Abbatiæ sancti Martini" names "genitoris nostri Rotberti quondam regis ac genitricis nostræ domnæ Beatricis" in his charter dated 26 Mar 931[67].

The marriage date is estimated by Werner on the assumption that the marriage accompanied the political reconciliation between Béatrix's father and Robert's uncle[68]. If the 907 donation mentioned above in fact refers to Robert's first wife, the marriage would of course have taken place after that date.

King Robert I & his first wife had one child:

1. [ADELA] (before 898-).

The Chronicle of Alberic de Trois-Fontaines refers to "comitis Heriberti gener…Roberti" and in a later passage to the sister of "dux Hugo Cappatus" as the wife of "comitis Heriberti de Peroni, Campanie et Veromandie" but does not name her[69].

Her origin is confirmed by Flodoard naming "Hugo dux cum nepotibus suis, Heriberti filiis" in 943[70].

Her birth date is estimated from the birth of her first child in [915]. Her name is deduced as follows. The 21 May 907 donation of Rebais abbey to the church of Paris refers to "comitis Rotberti et Adele comitisse"[71]. Although this phrasing usually indicates husband and wife, Settipani suggests that the chronology of the life of King Robert's son Hugues (attested as Robert's son by his second wife Béatrix) favours his birth, and therefore his father's second marriage, well before 907, which would mean "Adele" could not have been Robert's wife. This reasoning appears based firstly on Hugues already being married in [914], and secondly on the probability of his having reached the age of majority when he was recognised as duke in 922.

The 907 document is explained as referring to Robert and his elder daughter. The issue, however, is not beyond doubt, especially if the document in question was misdated.

m (before 21 May 907) HERIBERT II Comte de Vermandois, son of HERIBERT I Comte de Vermandois[-Carolingian] & his wife [Liedgardis] --- ([880]-23 Feb 943, bur Saint Quentin).

King Robert I & his [first/second] wife had one child:

2. EMMA (-2 Nov 934). Flodoard names "Emma regis Rotberti filia" when recording that she obliged Seulf Archbishop of Reims to consecrate her as queen at Reims in 923 in the absence of her husband fighting[72]. Rodulfus Glaber names "Emmam…sororem…magni Hugonis" as wife of "Rodulfus, Richardi ducis Burgundiæ filius", suggesting that she was instrumental in persuading her brother to support her husband's accession as king[73]. "Emme nostri imperii consortis" and "Emma coniux mea" is named in the charters of "Rodolfus Francorum rex" dated 21 Jun 931 and 1 Jul 931[74].

There is no indication whether Emma was born from her father's first or second marriage.

Flodoard records the death of "Emma regina" at the end of his passage dated 934[75]. The necrology of the abbey of Saint-Germain-des-Prés records the death "IV Non Nov" of "domna Emma regina"[76].

m ([911/19]%29 RODOLPHE [Raoul] Comte de Bourgogne, son of RICHARD “le Justicier” Duke of Burgundy & his wife Adélais d’Auxerre [Welf] (-Auxerre, Yonne 15/16 Jan 936, bur Abbaye de Sainte-Colombe de Sens).

He succeeded his father in 921 as Duke of Burgundy. He was elected as RAOUL King of France in 13 Jul 923 at Soissons to succeed his father-in-law, consecrated by Gautier Archbishop of Sens at the Abbey of Saint-Médard de Soissons.

King Robert I & his second wife had one child:

3. HUGUES ([898]-Dourdan, Essonne 16 Jun 956, bur église de l'Abbaye royale de Saint-Denis). He was installed as HUGUES "le Grand" Duc des Francs in 936.

--------------------------

From: http://www.francogene.com/quebec--genealogy/010/010408.php

The family of Robert Ier de FRANCE and Béatrice de VERMANDOIS

[10408] FRANCE (de), Robert Ier (..), roi

• married , from .. (France)

VERMANDOIS (de), Béatrice (Héribert Ier & .. [10409])

1) Hugues le Grand, died 956-06-17 or 956-07-01 Dourdan (Essonne : 910200), France, buried Saint-Denis (Seine-Saint-Denis : 930066), France, married Mayence ou Ingelheim (Germany) 938 Hedwidge de SAXE

Bibliographie : Mémoires (Société généalogique canadienne-française)

From the English Wikipedia page on Béatrice of Vermandois:

http://en.wikipedia.org/wiki/B%C3%A9atrice_of_Vermandois

Béatrice of Vermandois (c. 880 – after March 26, 931) was the daughter of Herbert I, Count of Vermandois.

Marriage and issue

She married in 895 Robert (d. 923), Marquis of Neustria, who became the King of France in 922. They had the following:

1. Emma, married around 918 to Rudolph, Duke of Burgundy, later King of France.

2. Hugh the Great, duke of the Franks, who was the father of Hugh Capet.

References

Patrick Van Kerrebrouck, Nouvelle histoire généalogique de l'auguste maison de France, vol. 1 : La Préhistoire des Capétiens (par Christian Settipani), 1993

Queen of Western Francia 922–923

Preceded by Eadgifu of England

Succeeded by Emma of France (daughter)

From http://www.rpi.edu/~holmes/Hobbies/Genealogy/ps03/ps03_444.htm

W.H.Turton, "The Plantagenet Ancestry" (Balt.:Gen.Pub.Co.,1968),p.112, gives Beatrix' mother as ______ "of France,"daughter of Robert the Strong, Count of Blois (ID1428). "Ancestral Roots..." (Balt., 1992) 53-18 gives her mother as Bertha de Morvois.

References: [Weis1],[AR7]

Béatrice of Vermandois (c. 880 – after March 26, 931) was the wife of Robert I, King of France . She is sometimes stated to be the sister of Herbert II, Count of Vermandois. No contemporary source explicitly states that Heribert II and Beatrix were the children of Herbert I, and researchers are divided on the probability of this relationship.
Marriage and issue: She married in 895 Robert (d. 923), Marquis of Neustria, who became the King of France in 922. They had the following:

Richilda of France

Hugh the Great, duke of the Franks, who was the father of Hugh Capet.

http://en.wikipedia.org/wiki/Béatrice_of_Vermandois