"contract (or agreement) between the publisher of the one part and (...) of the other." or "agreem
Sorry, running out of space:
"agreement between the publisher and ..."
The English language does not necessarily use the terms "(...) d'une part et (...) d'autre part. It sometimes uses only the names in a sentence such as "agreement between (...) and (...) without the equivalent of the French expression.
See for instance this translation from a Tax Court of Canada page:
"Le présent contrat est conclu entre, d'une part, Informix Software Inc. (« Informix »), une société du Delaware, et, d'autre part, CS Computing Services Inc. (le « licencié »), une société canadienne"
"This is an Agreement between Informix Software, Inc. ("Informix"), a Delaware corporation, and CS Computing Services, Inc. ("Licensee"), a Canadian corporation"
On the other hand, the words "of the one part" and "of the other part" are also very much in use:
"en vertu d'un certain contrat portant la date du 1er novembre 1934, passé entre l'association historique d'Annapolis-Royal, d'une part, et ledit Ewart Gladstone Morse, d'autre part; ce contrat étant dûment inscrit dans le registre des contrats pour le comté d'Annapolis"
"assigns, by a certain Indenture bearing date the 1st November, 1934, between The Historical Association of Annapolis Royal of the one part, and the said Ewart Gladstone Morse, of the other part, which said Indenture is duly recorded in the Registry of Deeds for the County of Annapolis"
Here is another example:
"The European Community, hereinafter referred to as "the Community", represented by the Commission of the European Communities, hereinafter referred to as "the Commission", and the European Investment Bank, hereinafter referred to as "the EIB",
of the one part,
and the Government of the Arab Republic of Egypt, hereinafter referred to as "Egypt",
of the other part, "
"Interim Agreement on trade and trade-related matters between the European Economic Community, and the European Coal and Steel Community, of the one part, and the Republic of Poland, of the other part"
You can use either, depending on the structure you choose for your sentence. I would try to use the more legal-sounding "of the one part, etc" expression.