The greatsword Hazirawn in Hoard of the Dragon Queen is described as "A sentient (neutral evil) greatsword" and it requires attunement. Are there any restrictions on who can attune to it, or any rules explaining what might happen if a good character attempts to attune to it?

Attunement is not alignment restricted unless the specific item says it is

There are no rules about who can attune to sentient magic items specifically, so the normal rules apply. If the item does not say that only a specific alignment can/can't attune to it, then any alignment can attune to it.

One example of this (as pointed out in Medix2's answer) is the Moonblade, which says:

(Requires Attunement by an Elf or Half-Elf of Neutral Good Alignment)

Hazirawn has nothing in it that would suggest any kind of alignment limitation on it, so any alignment can attune to it.

When the user conflicts with the item, the item can make demands

Now, as far as what happens when a user with a conflicting alignment does attune to it, the rules for sentient magic items do go into some detail:

A sentient item has a will of its own, shaped by its personality and alignment. If its wielder acts in a manner opposed to the item's alignment or purpose, conflict can arise. When such a conflict occurs, the item makes a Charisma check contested by the wielder's Charisma check. If the item wins the contest, it makes one or more of the following demands [list omitted]

So, while not explicitly limited to alignment based conflicts, it seems entirely likely that a user weilding a weapon that is in opposition to their alignment would come into conflict with that weapon's special purpose (if it has one) at some point and the rules describe how to deal with it (up to and including the item taking control of the user).

The Hoard of the Dragon Queen does not note any particular goals or behaviors of Hazirawn, but a DM can (and likely would) come up with some things to make it interesting.

Anybody can attune to this item

The section in the DMG on "Attunement" (page 138) states:

Some magic items require a creature to form a bond with them before their magical properties can be used. This bond is called attunement, and certain items have a prerequisite for it.

When an item has restrictions/prerequisites on who can attune to it they are listed in its description, for example the Moonblade states:

(Requires Attunement by an Elf or Half-Elf of Neutral Good Alignment)

The Rod of the Pact Keeper states:

(Requires Attunement by a Warlock)

The Hazirawn, however, only states:

(Requires Attunement)

There are no further requirements, so anybody can attune to this.

Additionally, as user @Rubiksmoose points out in their answer, there are rules for what happens when conflicts arise with sentient weapons:

A sentient item has a will of its own, shaped by its personality and alignment. If its wielder acts in a manner opposed to the item's alignment or purpose, conflict can arise. When such a conflict occurs, the item makes a Charisma check contested by the wielder's Charisma check. If the item wins the contest, it makes one or more of the following demands...