If you want to send or receive fax via the internet then you need an online fax or fax to email service. There's no free software that will allow you to do this because you need a provider that will do this for you. Like you can not dial and make calls from your computer directly, you need a VoIP provider for that.
You mentioned you don't have a fax modem/dial up modem so there's no way to send fax too through your phone line from your computer.
Just search for internet fax services and you probably find one that suits you. If you don't intend to send out hundreds a day then check out Onesuite online fax service
. It's 2.5c per page plus $2.95/monthly. You can receive unlimited fax too just in case you need to.