Personally, I would point the A record to the same server. No need to touch the CNAME (in this case, or indeed, many cases). Very simply: CNAME is basically an alias, a forwarder. So, a request comes in to the registrar, hits the CNAME which looks up the relevant A record. Now a days, we just create more A records so we can avoid the CNAME look up, the result is the same (if not microseconds faster).
Also, do remember, that a site can take up to 72 hours for DNS changes to take place. I've made changes before and my work machine would not see the results, but, my home PC did (I used a different ISP to the company) meaning, until the company DNS caught up, I had to log on to my home PC to see the new website.
General comments now, which may not be useful for you but may be for other visitors:
Now, it depends on what content is being used? Will example.net and exmaple.com be showing the same website (and therefore the same content)? If so use 301 perm redirects or using canonical links can help the search engines knows that the data is the same for both sites, but which to favour.
If they are doing something such as showing variations, or locale specific, then you can show
<link rel="alternate" href="http://example.com/net" hreflang="en-gb" />.
However, if the content is the same, you need to ask yourself, what is the point? You already have example.com so why do you need to use example.net? If you are migrating from example.com to example.net then fine, it makes sense to use the redirect methods described above, but, if you are buying the domain names just so competitors can't buy similar domain names to you, then leave them, doing nothing! This way, people won't start linking to variations of your site which could cause issues at a later stage (it's easier to deal with 1 domain instead of several).