It is a great question.
Your first problem: You have no contacts.
Knowing who to contact is often the golden question. Being heard or actually making contact is another. In a large company that sort of information or avenue in, is well protected information. That is partly why the so called 'well connected' people can make such inroads so quickly when bringing a new product or service to market. It really is who you know and not just what you know.
The second: They probably know.
It is probably the case that they know everything you are about to tell them, but either they are ignoring it because of timing, strategic issues, complications with other back end systems, IT restructuring, parent company control, budgeting issues, or a thousand other reasons.
The third: They will not use you.
You may present the idea, maybe even trigger an upgrade cycle or process, but they will not use you. They will use a service provider used to dealing at scale, that can provide a contractual and perhaps national support service that one man cannot offer. Or they will use the internal systems provider that can tie the website into their back-ends seamlessly.
The fourth: They will almost certainly want more than a fix.
As soon as the fix issue comes around to be dealt with, there will be other voices calling for account integration, online services and sales, internationalization, seo and social media campaigns to work hand in hand with the website development. It will become a big project and will take time to get the budget in place to support it.
Dealing with a big company is a notoriously difficult thing to do, unless you have a way in, a recommendation, a contact in the company or a reference from another corporate customer of yours of equal or greater standing than them. Even then you still may not survive the tender process, or it might all get done in house.
A way forward?
Your only solution is to first produce a value added plan that addresses the main thing they are concerned about. Potential return on investment. What can you offer that will help them to generate more income. It needs to be in one big package, with a fixed price tag, that answers all their questions and has elements they cannot do themselves and is not available from other providers. You need to think up something unique only you can offer.
Then you need to find them, at exhibitions, at shows, track them down online, visit their offices, send a free gift to someone to open up a conversation, find out who could help you get in there, and make contact to them. Make the package something they can tout as a great thing they achieved, give them something to buy into. Only then will you have a hook that might help you get in front of the decision makers.
Or, wait until they realize and a tender is put to market. Unfortunately dealing with a multinational is like dealing with a government, nothing will happen quickly, and nothing will happen without a really good look at the markets, the existing service providers, and as part of a much bigger long term plan.
Sorry if that is not what you wanted to hear. I would estimate you have a <0.5% chance of getting into a position to help them. Sorry.
It is frustrating, my phone providers website is so awful I refuse to use it. But I would not waste my time trying to get in there to fix it or improve it for them. It would be like flogging a dead horse.