Add a trace appender to log4net which would write into the Trace and make sure you have azure diagnostics trace listner configured
As indicated below in you config file it should have
<log4net>
<appender name="TraceAppender1" type="log4net.Appender.TraceAppender">
<layout type="log4net.Layout.PatternLayout">
<param name="ConversionPattern" value="%d [%t],[%c],[%p], %m%n" />
</layout>
</appender>
<root>
<level value="DEBUG" />
<appender-ref ref="TraceAppender1" />
</root>
</log4net>
<system.diagnostics>
<trace autoflush="true" indentsize="4" >
<listeners>
<add type="Microsoft.WindowsAzure.Diagnostics.DiagnosticMonitorTraceListener, Microsoft.WindowsAzure.Diagnostics, Version=1.0.0.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35"
name="AzureDiagnostics">
<filter type="" />
</add>
</listeners>
</trace>
</system.diagnostics>