# Não está apresentando o erro de validação. A parte do envio de email removi para o código não ficar grande, mas está funcionando normal.
# Form
defmodule Teste.Forms.Contact do
  use Ecto.Schema
  import Ecto.Changeset

  schema "embedded_schema" do
    field :email, :string
    field :name, :string
    field :message, :binary
  end

  def changeset(model, attrs) do
    model
    |> cast(attrs, [:email, :name, :message])
    |> validate_required([:email, :name, :message])
    |> validate_length(:message, min: 10)
  end
end

# Controller
def send_email(conn, %{"contact" => contact_params}) do
    changeset = Contact.changeset(%Contact{}, contact_params)
    render(conn, "index.html", changeset: changeset)
end

# Formulário
<%= form_for @changeset, Routes.page_path(@conn, :send_email), [method: "post"], fn f -> %>
  <%= if @changeset.action do %>
    <div class="alert alert-danger">
      <p>Oops, something went wrong! Please check the errors below.</p>
    </div>
  <% end %>
  <div class="row">
    <div class="col-sm-12">
      <%= text_input f, :name, [placeholder: "Nome", class: "form-control", required: true] %>
      <%= error_tag f, :name %>
    </div>
    <div class="col-sm-12">
      <%= email_input f, :email, [placeholder: "E-mail", class: "form-control", required: true] %>
      <%= error_tag f, :email %>
    </div>
  </div>
  <div class="form-group">
    <%= textarea f, :message, [placeholder: "Mensagem", class: "form-control", required: true] %>
    <%= error_tag f, :message %>
  </div>
  <%= submit "Enviar", [class: "btn btn-block"] %>
<% end %>