Short answer - yes it can help, but only with touch spells and/or spells with an attack roll.
Long answer is a little too broad, but I think it is important in the context.
How do you get a familiar
First and foremost, you get familiar either from the Find Familiar spell (a Wizard's one), or from a class feature (like Warlock's Pact of Chain). Normally a 1-st level Bard cannot have a familiar, unless you get one of the specific feats. You might get it at 10th level though, with the "Magical Secrets" Bard feature.
You don't control the familiar directly
You can find a familiar description in the Player's Handbook, page 240:
Your familiar acts independently of you, but it always
obeys your commands. In combat, it rolls its own
initiative and acts on its own turn.
It says the familiar "acts independently", so your character have no direct control over it (they can give it orders tho). You should discuss it with the DM to what extend you will directly control the familiar as a player.
What a familiar can do
Usually, being a Wizard, you get the following advantages from the familiar:
- It can deliver your spells with the "touch" range, using your spell attack bonus.
- It can communicate with you telepathically (but keep in mind, most familiars don't know any language).
- You can share its senses (vision and hearing) for 6 seconds. If you're blinded, you can use Familiar's senses to cast a spell that requires you to "see the target".
- It can do other things a creature of its type can do (with the DM approval), except of the attacking. This includes the "Help action".
What a familiar can't do
- It can't attack
- It can't cast your spells
- It can't maintain a concentration for you
- It can't raise your spell DC
The Help action
PHB states that a familiar "can take other actions as normal":
A familiar can't attack, but it can take other actions as normal.
This can include any efforts of helping your allies. If it is a familiar, is irrelevant in this case. Any creature can help its allies.
PHB describes two usual cases.
- Help with an ability check:
You can lend your aid to another creature in the completion of a task. When you take the Help action, the creature you aid gains advantage on the next ability check it makes to perform the task you are helping with, provided that it makes the check before the start of your next turn.
There are restrictions though, see more in the "Working together" chapter.
- Help in combat:
... you can aid a friendly creature in attacking a creature within 5 feet of you. You feint, distract the target, or in some other way team up to make your ally’s attack more effective. If your ally attacks the target before your next turn, the first attack roll is made with advantage.
Emphasis mine - the familiar shouldn't just "be within 5 feet" and take a unclear "help action" in order to magically give you an advantage. The familiar do things - it shouts, fusses around, meddles with the enemy, pours out sand over enemy's head, you name it. Mechanically, it's always the DM who ultimately decides if there was an advantage.
A familiar (and most of the creatures) isn't a mechanical robot, capable only of several pre-defined actions. You character can do other actions as well. The DM says, what check you should make (if any):
When you describe an action not detailed elsewhere in the rules, the GM tells you whether that action is possible and what kind of roll you need to make, if any, to determine success or failure.
What a familiar could do, for example:
- Fetch you an item
- Being a messenger
- Being a scout
- Perform tricks