A manuscript called The Chronicle of Battle Abbey tells this story that took place during :
When William, duke of Normandy, looked from the high ground of Telham Hill upon the forces of King Harold, he vowed that if God gave him the victory he would found a monastery upon the place of battle. Amongst those who heard this vow was a monk of Marmoutier, William called 'the smith,' who when William had obtained the crown of England urged him to fulfil his promise; the king willingly agreed and entrusted William with the execution of his design.
The monk, therefore, brought over from Marmoutier four of his brethren, but as the actual site of the battle seemed to them unsuitable for a great monastery, they began to build on the lower ground to the west. When the Conqueror heard of this he angrily insisted that the foundations should rest upon the very spot where he had achieved his victory, and upon the monks pleading a scarcity of water he replied, 'If God spare my life I will so amply provide for this place that wine shall be more abundant here than water is in any other great abbey.'
... For various reasons, however, building progressed slowly, and it was not until 1076 that things were sufficiently advanced for an abbot to be appointed. Robert Blancard, one of the four monks who had first come over, was elected, but on his way back from Marmoutier he was drowned. Accordingly William 'the smith' was sent to Marmoutier to fetch Gausbert, who came with four of his brethren and was consecrated abbot of St. Martin's of the place of Battle.
In Heads of Religious Houses: England and Wales 940–1216, the authors compile lists of abbots, etc., that include Battle Abbey. From their research, Robert Blanchard was the first abbot, starting in 1067. He had previously been a monk at Marmoutier Abbey. Marmoutier Abbey was founded in 327 CE by St. Martin of Tours, which explains why Battle Abbey was dedicated to Martin.
Pope Alexander II telling William to do penance for all the souls killed in the battle is true. Battle Abbey being built "on the lower ground to the west" away from Senlac Hill where the fighting actually took place is accurate. A conversation in the middle of a huge battle between the leader of one side and a monk hanging out is ... less likely. Making sure there is a compelling story behind the founding of the abbey to enhance your reputation ... priceless.