The problem you're having is an issue with the rules of DNS, which forbid a CNAME record where another record exists. The naked address (or Apex) example.com already has two records (the SOA and NS) so a CNAME is not allowed.
If a CNAME RR is present at a node, no other data should be
present; this ensures that the data for a canonical name and its aliases
cannot be different. This rule also insures that a cached CNAME can be
used without checking with an authoritative server for other RR types.
In order to create an Apex record, i.e. example.com you need to use an A record, which means it needs to point to the IP of your Azure website. Once you have that you can then create a CNAME from www to example.com. (this is the supported method - your IP Address for Azure websites is static)
the command you are looking for, would be something like
$rs = New-AzureRmDnsRecordSet -Name "@" -RecordType A `
-ZoneName example.com -ResourceGroupName $RG `
-Ttl $ttl -Force -Overwrite
Add-AzureRmDnsRecordConfig -RecordSet $rs -Ipv4Address $IPAddress
Set-AzureRmDnsRecordSet -RecordSet $rs -Overwrite
then
$rs = New-AzureRmDnsRecordSet -Name "www" -RecordType "CNAME" `
-ZoneName "something.com" -ResourceGroupName "DNSRecords" `
-Ttl 60 -Overwrite -Force
Add-AzureRmDnsRecordConfig -RecordSet $rs -Cname "example.com"
Set-AzureRmDnsRecordSet -RecordSet $rs -Overwrite
If you don't have an IP address to point your apex A record to then the only solution you have is to use an IP address that will provide HTTP redirect for you.
The simplest way I can think of doing this would be to create a small Azure Web App and use that IP Address to send a HTTP status 301 Moved Permanently header. This would place negligible load on the server because it wouldn't actually be serving any pages.
An alternative would be switching to a DNS provider that does provide apex CNAME (or at least a workaround to provide similar functionality)
There are also some HTTP redirect services (both free and paid) at the end of a search (However I've never used any of these so I can't comment on the quality!)