Problem : declare a mapping and use it in your openapi.yml file The cloudformation :
AWSTemplateFormatVersion: '2010-09-09'
Transform: 'AWS::Serverless-2016-10-31'
Parameters:
  Env:
    Type: String
    Default: dev
    AllowedValues:
      - sandbox
      - dev
      - test
      - prod

Mappings:
  CDN:
    prod:
      value: https://media.arnaudcharlier.be
    test:
      value: https://media-test.arnaudcharlier.be
    dev:
      value: https://1afezfe124djezs.cloudfront.net
    sandbox:
      value: https://d1rz2vdzdzdzafezs.cloudfront.net

Resources:
  ###############
  # API Gateway #
  ###############

  ApiGateway:
    Type: AWS::Serverless::Api
    Properties:
      Name: !Sub media-api
      StageName: !Sub ${Env}
      EndpointConfiguration: REGIONAL
      DefinitionBody:
        Fn::Transform:
          Name: 'AWS::Include'
          Parameters:
            Location: ./openapi.yml
openapi.yml
openapi: 3.0.0
servers: []
info:
  version: "2.0"
  title: Media MicroService endpoint documentation
 x-definitions:
  enums:
    Status:
      enum: &Status [INITIATED, SAVED, PUBLISHED, UNPUBLISHED]
    GrabStatus:
      enum: &GrabStatus [STARTED, IN_PROCESS, ERROR, VALID, SKIP]
  
paths:
  /{objectType}/{objectId}/{fileType}:
    get:
      tags:
        - Cars
      summary: Retrieve all media of a type for a given objectId
      security:
        - api_key: []
      parameters:
        - name: objectType
          in: path
          description: Object type 
          required: true
          schema:
            type: string
        - name: objectId
          in: path
          description: ID of the object
          required: true
          schema:
            type: integer
        - name: fileType
          in: path
          required: true
          description: File type (pictures, pdfs or videos)
          schema:
            type: string
        - name: source
          in: query
          required: false
          description: full or raw (default to full)
          schema:
            type: string
        - name: path
          in: query
          required: false
          description: absolute or relative (default to absolute)
          schema:
            type: string
      responses:
        '200':
          description: OK
          content:
            application/vnd.be.media.pictures.v2+json:
              schema:
                type: array
                items:
                  $ref: '#/components/schemas/Picture'
      x-amazon-apigateway-integration:
        httpMethod: POST
        type: aws_proxy
        uri:
          Fn::Sub: "arn:aws:apigateway:${AWS::Region}:lambda:path/2015-03-31/functions/${GetMedia.Arn}/invocations"
    post:
      tags:
        - Classifieds
      summary: Create new media for a given Object ID
      security:
        - api_key: []
      parameters:
        - name: key
          in: query
          description: Bucket key (ex classifieds/14567/image.png)
          required: true
          schema:
            type: string
        - name: Content-Type
          in: header
          description: Content type
          required: true
          schema:
            type: string
        - name: Content-Length
          in: header
          description: Content length
          required: true
          schema:
            type: string
      requestBody:
        description: File to be uploaded
        required: true
        content:
          image/png:
            schema:
              type: string
              format: binary
          image/jpeg:
            schema:
              type: string
              format: binary
          video/x-msvideo:
            schema:
              type: string
              format: binary
          application/pdf:
            schema:
              type: string
              format: binary
      responses:
        '204':
          description: OK
          headers:
            Content-Type:
              schema:
                type: string
            Content-Length:
              schema:
                type: string
            ETag:
              schema:
                type: string
            X-CDN:
              schema:
                type: string

        '400':
          description: Error - Bad request
          headers:
            Content-Type:
              schema:
                type: string
            Content-Length:
              schema:
                type: string
        '415':
          description: Error - Unsupported media type
          headers:
            Content-Type:
              schema:
                type: string
            Content-Length:
              schema:
                type: string
        '500':
          description: Error - Internal error
          headers:
            Content-Type:
              schema:
                type: string
            Content-Length:
              schema:
                type: string
      x-amazon-apigateway-integration:
        credentials:
          Fn::GetAtt:
            - ApiGatewayWriteS3Role
            - Arn
        uri:
          Fn::Sub: arn:aws:apigateway:${AWS::Region}:s3:path/{bucket}/{key}
        passthroughBehavior: when_no_match
        httpMethod: PUT
        type: aws
        requestParameters:
          integration.request.header.Content-Length: method.request.header.Content-Length
          integration.request.header.Content-Type: method.request.header.Content-Type
          integration.request.path.bucket:
            Fn::Sub:
              - "'${Bucket}'"
              - Bucket:
                  Fn::FindInMap:
                    - 'MediaBucketName'
                    - Ref: 'Env'
                    - 'value'
          integration.request.path.key: method.request.querystring.key
        responses:
          default:
            statusCode: 204
            responseParameters:
              method.response.header.Content-Type: integration.response.header.Content-Type
              method.response.header.Content-Length: integration.response.header.Content-Length
              method.response.header.ETag: integration.response.header.ETag
              method.response.header.X-CDN:
                Fn::Sub:
                  - "'${CDN}'"
                  - CDN:
                      Fn::FindInMap:
                        - 'CDN'
                        - Ref: 'Env'
                        - 'value'
          '4\\d{2}':
            statusCode: 400
          '5\\d{2}':
            statusCode: 500