You need to say the field you want to call (in the ViewFields). The final request should look like this :
<soap:Envelope xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:soap="http://schemas.xmlsoap.org/soap/envelope/">
<soap:Body>
<GetListItems xmlns="http://schemas.microsoft.com/sharepoint/soap/">
<listName>My Documents List</listName>
<viewName></viewName>
<query><Query></Query></query>
<viewFields>
<ViewFields Properties="True">
<FieldRef Name="FileLeafRef"></FieldRef>
<FieldRef Name="File_x0020_Size"></FieldRef>
</ViewFields>
</viewFields>
<rowLimit>0</rowLimit>
<queryOptions>
<QueryOptions>
<DateInUtc>True</DateInUtc>
<Paging ListItemCollectionPositionNext=""></Paging>
<ViewAttributes Scope="Recursive"></ViewAttributes>
<IncludeAttachmentUrls>True</IncludeAttachmentUrls>
<IncludeMandatoryColumns>False</IncludeMandatoryColumns>
<ExpandUserField>False</ExpandUserField>
</QueryOptions>
</queryOptions>
</GetListItems>
</soap:Body>
</soap:Envelope>