First of all, I would argue that corporations do not necessarily believe in free enterprise. Instead, corporations believe in free enterprise so far as it is beneficial to them. This is an important distinction. It explains why corporations would support the idea of government intervention in the economy.
Free enterprise is not necessarily a good thing for corporations. The reason for this is that free enterprise entails competition. Whenever there is free enterprise, companies have to compete with one another for customers. This is not something that companies particularly like. Companies would prefer to have customers who have to buy from them. They would prefer to have predictable (and preferably limited) competition. When companies have to compete, it puts them in danger. Companies that have to compete can be defeated in the competition and can lose profit and can even lose their existence. For example, Pan-American Airways was one of the biggest and most prestigious airlines in the world for a long time. When it started to have to compete more with other airlines, it failed and it no longer exists today. Companies do not want to risk this if they can avoid it.
This is why companies support government intervention. If they already have a good position in their market, they will generally want the government to protect them from competition. They will also want the government to help them be more profitable. For this reason, they will be in favor of things like government tax breaks or subsidies for their businesses.
Companies do not like the competition and uncertainty that comes with free enterprise. They would prefer to have the government protect them from competition and/or help them through subsidies and other such things. They prefer this because it makes them more likely to be profitable and less likely to lose out due to competition.