The Jean Arnold in the Swiss Overseas Emigration database was born in 1905. However, there's a Jean Arnold born c. 1877 in the New York Passengers List database:

Name: Jean Arnold
Arrival Date: 20 Feb 1900
Estimated Birth Year: abt 1877
Age: 23
Gender: Male
Port of Departure: Havre
Ethnicity/Race-
/Nationality: Swedish
Ship Name: La Touraine
Search Ship Database: View the La Touraine in the 'Passenger Ships and Images' database
Port of Arrival: New York, New York
Line: 17
Microfilm Serial: 15
Microfilm Roll: T715_103
Page Number: 153

Also, looks as if he was traveling with his cousin, Jeanne Arnold. There's more info on the manifest. Do you have access to this database?