I think that, since these are horizontal elements of the foundation, they need to be called 'beams'. This is because 'piles' are usually understood to be vertical poles driven into the ground. You could add 'foundation' in there (cross- and longitudinal foundation beams), just to clarify that these are beams used for the foundation.
See:
http://en.wikipedia.org/wiki/Deep_foundation#Pile_foundation...
There are different terms used to describe different types of deep foundations including the pile (which is analogous to a pole), the pier (which is analogous to a column), drilled shafts, and caissons. Piles are generally driven into the ground in situ; other deep foundations are typically put in place using excavation and drilling. The naming conventions may vary between engineering disciplines and firms. Deep foundations can be made out of timber, steel, reinforced concrete and prestressed concrete.

and:

http://nl.wikipedia.org/wiki/Langshout_(fundering)
Langshout (fundering)Uit Wikipedia, de vrije encyclopedie
Ga naar: navigatie, zoeken Het langshout is een balk die horizontaal over de koppen van funderingspalen wordt gelegd. Hier bovenop worden de dragende muren van een gebouw geconstrueerd.

This is typical in Amsterdam and Rotterdam. See:

Building construction - Our Lord in the Attic: A Case Studywww.getty.edu › ... › BuildingEn cache - Traduire cette page
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Since Amsterdam is located on a bog, houses are built on a typical foundation of wooden poles. Long wooden beams, basically entire trees of 13 to 20 meters ...

Building a house in Amsterdam - World Architecture Images ...www.european-architecture.info/.../AMS-TYP-H...En cache - Traduire cette page
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This is particularly the case in Amsterdam because of the high level of the ground water ... The wooden foundation had to be kept submerged beneath the ground water ... A temporary work floor was placed on top of the floor beams so that the ...


and here you will find reference made to cross- and longitudinal beams, which is what I think is referred to in the Dutch text.

[PDF]
Chapter 2 Bacterial wood decay in Europe - Shrwww.shr.nl/wp-content/uploads/.../chapter2.pdf - Traduire cette page
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The system with cross- and longitudinal beams gave .... In the period from 1997 to 2004 SHR analysed more than 4000 wood sample originated from foundation ...


GehrTec® Base - Gehrlicher Solarwww.gehrlicher.com/.../EN_112803_tQ_GehrTec... - Traduire cette page
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consisting of posts, cross and longitudinal beams, module girders, ... she has performed an initial testing of the a. m. properties ofthe kits and the results fulfil the ...